Markov Renewal And Piecewise Deterministic Processes

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Markov Renewal and Piecewise Deterministic Processes

Author : Christiane Cocozza-Thivent
Publisher : Springer Nature
ISBN 13 : 3030704475
Total Pages : 252 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Markov Renewal and Piecewise Deterministic Processes by : Christiane Cocozza-Thivent

Download or read book Markov Renewal and Piecewise Deterministic Processes written by Christiane Cocozza-Thivent and published by Springer Nature. This book was released on 2021-06-09 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed at researchers, graduate students and engineers who would like to be initiated to Piecewise Deterministic Markov Processes (PDMPs). A PDMP models a deterministic mechanism modified by jumps that occur at random times. The fields of applications are numerous : insurance and risk, biology, communication networks, dependability, supply management, etc. Indeed, the PDMPs studied so far are in fact deterministic functions of CSMPs (Completed Semi-Markov Processes), i.e. semi-Markov processes completed to become Markov processes. This remark leads to considerably broaden the definition of PDMPs and allows their properties to be deduced from those of CSMPs, which are easier to grasp. Stability is studied within a very general framework. In the other chapters, the results become more accurate as the assumptions become more precise. Generalized Chapman-Kolmogorov equations lead to numerical schemes. The last chapter is an opening on processes for which the deterministic flow of the PDMP is replaced with a Markov process. Marked point processes play a key role throughout this book.

Telegraph Processes and Option Pricing

Author : Nikita Ratanov
Publisher : Springer Nature
ISBN 13 : 3662658275
Total Pages : 451 pages
Book Rating : 4.6/5 (626 download)

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Book Synopsis Telegraph Processes and Option Pricing by : Nikita Ratanov

Download or read book Telegraph Processes and Option Pricing written by Nikita Ratanov and published by Springer Nature. This book was released on 2023-01-04 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an extensive, systematic overview of the modern theory of telegraph processes and their multidimensional counterparts, together with numerous fruitful applications in financial modelling. Focusing on stochastic processes of bounded variation instead of classical diffusion, or more generally, Lévy processes, has two obvious benefits. First, the mathematical technique is much simpler, which helps to concentrate on the key problems of stochastic analysis and applications, including financial market modelling. Second, this approach overcomes some shortcomings of the (parabolic) nature of classical diffusions that contradict physical intuition, such as infinite propagation velocity and infinite total variation of paths. In this second edition, some sections of the previous text are included without any changes, while most others have been expanded and significantly revised. These are supplemented by predominantly new results concerning piecewise linear processes with arbitrary sequences of velocities, jump amplitudes, and switching intensities. The chapter on functionals of the telegraph process has been significantly expanded by adding sections on exponential functionals, telegraph meanders and running extrema, the times of the first passages of telegraph processes with alternating random jumps, and distribution of the Euclidean distance between two independent telegraph processes. A new chapter on the multidimensional counterparts of the telegraph processes is also included. The book is intended for graduate students in mathematics, probability, statistics and quantitative finance, and for researchers working at academic institutions, in industry and engineering. It can also be used by university lecturers and professionals in various applied areas.

Statistical Inference for Piecewise-deterministic Markov Processes

Author : Romain Azais
Publisher : John Wiley & Sons
ISBN 13 : 1119544033
Total Pages : 279 pages
Book Rating : 4.1/5 (195 download)

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Book Synopsis Statistical Inference for Piecewise-deterministic Markov Processes by : Romain Azais

Download or read book Statistical Inference for Piecewise-deterministic Markov Processes written by Romain Azais and published by John Wiley & Sons. This book was released on 2018-07-31 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Piecewise-deterministic Markov processes form a class of stochastic models with a sizeable scope of applications: biology, insurance, neuroscience, networks, finance... Such processes are defined by a deterministic motion punctuated by random jumps at random times, and offer simple yet challenging models to study. Nevertheless, the issue of statistical estimation of the parameters ruling the jump mechanism is far from trivial. Responding to new developments in the field as well as to current research interests and needs, Statistical inference for piecewise-deterministic Markov processes offers a detailed and comprehensive survey of state-of-the-art results. It covers a wide range of general processes as well as applied models. The present book also dwells on statistics in the context of Markov chains, since piecewise-deterministic Markov processes are characterized by an embedded Markov chain corresponding to the position of the process right after the jumps.

Point Process Theory and Applications

Author : Martin Jacobsen
Publisher : Springer Science & Business Media
ISBN 13 : 0817644636
Total Pages : 325 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Point Process Theory and Applications by : Martin Jacobsen

Download or read book Point Process Theory and Applications written by Martin Jacobsen and published by Springer Science & Business Media. This book was released on 2006-07-27 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematically rigorous exposition of the basic theory of marked point processes and piecewise deterministic stochastic processes Point processes are constructed from scratch with detailed proofs Includes applications with examples and exercises in survival analysis, branching processes, ruin probabilities, sports (soccer), finance and risk management, and queueing theory Accessible to a wider cross-disciplinary audience

Constructive Computation in Stochastic Models with Applications

Author : Quan-Lin Li
Publisher : Springer Science & Business Media
ISBN 13 : 364211492X
Total Pages : 693 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Constructive Computation in Stochastic Models with Applications by : Quan-Lin Li

Download or read book Constructive Computation in Stochastic Models with Applications written by Quan-Lin Li and published by Springer Science & Business Media. This book was released on 2011-02-02 with total page 693 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Constructive Computation in Stochastic Models with Applications: The RG-Factorizations" provides a unified, constructive and algorithmic framework for numerical computation of many practical stochastic systems. It summarizes recent important advances in computational study of stochastic models from several crucial directions, such as stationary computation, transient solution, asymptotic analysis, reward processes, decision processes, sensitivity analysis as well as game theory. Graduate students, researchers and practicing engineers in the field of operations research, management sciences, applied probability, computer networks, manufacturing systems, transportation systems, insurance and finance, risk management and biological sciences will find this book valuable. Dr. Quan-Lin Li is an Associate Professor at the Department of Industrial Engineering of Tsinghua University, China.

Stochastic Reliability and Maintenance Modeling

Author : Tadashi Dohi
Publisher : Springer Science & Business Media
ISBN 13 : 1447149718
Total Pages : 375 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Stochastic Reliability and Maintenance Modeling by : Tadashi Dohi

Download or read book Stochastic Reliability and Maintenance Modeling written by Tadashi Dohi and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: In honor of the work of Professor Shunji Osaki, Stochastic Reliability and Maintenance Modeling provides a comprehensive study of the legacy of and ongoing research in stochastic reliability and maintenance modeling. Including associated application areas such as dependable computing, performance evaluation, software engineering, communication engineering, distinguished researchers review and build on the contributions over the last four decades by Professor Shunji Osaki. Fundamental yet significant research results are presented and discussed clearly alongside new ideas and topics on stochastic reliability and maintenance modeling to inspire future research. Across 15 chapters readers gain the knowledge and understanding to apply reliability and maintenance theory to computer and communication systems. Stochastic Reliability and Maintenance Modeling is ideal for graduate students and researchers in reliability engineering, and workers, managers and engineers engaged in computer, maintenance and management works.

Engineering Reliability and Risk Assessment

Author : Harish Garg
Publisher : Elsevier
ISBN 13 : 0323913830
Total Pages : 284 pages
Book Rating : 4.3/5 (239 download)

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Book Synopsis Engineering Reliability and Risk Assessment by : Harish Garg

Download or read book Engineering Reliability and Risk Assessment written by Harish Garg and published by Elsevier. This book was released on 2022-09-23 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engineering Reliability and Risk Assessment explains how to improve the performance of a system using the latest risk and reliability models. Against a backdrop of increasing availability of industrial data, and ever-increasing global commercial competition, the standards for optimal efficiency with minimum hazards keep improving. Topics explained include Effective strategies for the maintenance of the mechanical components of a system, How to schedule necessary interventions throughout the product life cycle, How to understand the structure and cost of complex systems, Planning a schedule to improve the reliability and life of the system, software, system safety and risk informed asset management, and more. - Uses case studies from industry practice to explain innovative solutions to real world risk assessment problems - Addresses the full interdisciplinary range of topics that influence this complex field - Provides brief introductions to important concepts, including risk and reliability analysis and fuzzy reliability

Statistical Inference for Piecewise-deterministic Markov Processes

Author : Romain Azais
Publisher : John Wiley & Sons
ISBN 13 : 1786303027
Total Pages : 300 pages
Book Rating : 4.7/5 (863 download)

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Book Synopsis Statistical Inference for Piecewise-deterministic Markov Processes by : Romain Azais

Download or read book Statistical Inference for Piecewise-deterministic Markov Processes written by Romain Azais and published by John Wiley & Sons. This book was released on 2018-08-14 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Piecewise-deterministic Markov processes form a class of stochastic models with a sizeable scope of applications: biology, insurance, neuroscience, networks, finance... Such processes are defined by a deterministic motion punctuated by random jumps at random times, and offer simple yet challenging models to study. Nevertheless, the issue of statistical estimation of the parameters ruling the jump mechanism is far from trivial. Responding to new developments in the field as well as to current research interests and needs, Statistical inference for piecewise-deterministic Markov processes offers a detailed and comprehensive survey of state-of-the-art results. It covers a wide range of general processes as well as applied models. The present book also dwells on statistics in the context of Markov chains, since piecewise-deterministic Markov processes are characterized by an embedded Markov chain corresponding to the position of the process right after the jumps.

Stochastic Processes for Insurance and Finance

Author : Tomasz Rolski
Publisher : John Wiley & Sons
ISBN 13 : 0470317884
Total Pages : 680 pages
Book Rating : 4.4/5 (73 download)

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Book Synopsis Stochastic Processes for Insurance and Finance by : Tomasz Rolski

Download or read book Stochastic Processes for Insurance and Finance written by Tomasz Rolski and published by John Wiley & Sons. This book was released on 2009-09-25 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Processes for Insurance and Finance offers a thorough yet accessible reference for researchers and practitioners of insurance mathematics. Building on recent and rapid developments in applied probability, the authors describe in general terms models based on Markov processes, martingales and various types of point processes. Discussing frequently asked insurance questions, the authors present a coherent overview of the subject and specifically address: The principal concepts from insurance and finance Practical examples with real life data Numerical and algorithmic procedures essential for modern insurance practices Assuming competence in probability calculus, this book will provide a fairly rigorous treatment of insurance risk theory recommended for researchers and students interested in applied probability as well as practitioners of actuarial sciences. Wiley Series in Probability and Statistics

Stochastic Systems In Merging Phase Space

Author : Vladimir S Koroliuk
Publisher : World Scientific
ISBN 13 : 9814479012
Total Pages : 348 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Stochastic Systems In Merging Phase Space by : Vladimir S Koroliuk

Download or read book Stochastic Systems In Merging Phase Space written by Vladimir S Koroliuk and published by World Scientific. This book was released on 2005-12-21 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides recent results on the stochastic approximation of systems by weak convergence techniques. General and particular schemes of proofs for average, diffusion, and Poisson approximations of stochastic systems are presented, allowing one to simplify complex systems and obtain numerically tractable models.The systems discussed in the book include stochastic additive functionals, dynamical systems, stochastic integral functionals, increment processes and impulsive processes. All these systems are switched by Markov and semi-Markov processes whose phase space is considered in asymptotic split and merging schemes. Most of the results from semi-Markov processes are new and presented for the first time in this book.

Mathematical Methods in Survival Analysis, Reliability and Quality of Life

Author : Catherine Huber
Publisher : John Wiley & Sons
ISBN 13 : 1118624114
Total Pages : 294 pages
Book Rating : 4.1/5 (186 download)

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Book Synopsis Mathematical Methods in Survival Analysis, Reliability and Quality of Life by : Catherine Huber

Download or read book Mathematical Methods in Survival Analysis, Reliability and Quality of Life written by Catherine Huber and published by John Wiley & Sons. This book was released on 2013-03-01 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reliability and survival analysis are important applications of stochastic mathematics (probability, statistics and stochastic processes) that are usually covered separately in spite of the similarity of the involved mathematical theory. This title aims to redress this situation: it includes 21 chapters divided into four parts: Survival analysis, Reliability, Quality of life, and Related topics. Many of these chapters were presented at the European Seminar on Mathematical Methods for Survival Analysis, Reliability and Quality of Life in 2006.

Applied Nonparametric Statistics in Reliability

Author : M. Luz Gámiz
Publisher : Springer Science & Business Media
ISBN 13 : 0857291181
Total Pages : 238 pages
Book Rating : 4.8/5 (572 download)

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Book Synopsis Applied Nonparametric Statistics in Reliability by : M. Luz Gámiz

Download or read book Applied Nonparametric Statistics in Reliability written by M. Luz Gámiz and published by Springer Science & Business Media. This book was released on 2011-02-14 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonparametric statistics has probably become the leading methodology for researchers performing data analysis. It is nevertheless true that, whereas these methods have already proved highly effective in other applied areas of knowledge such as biostatistics or social sciences, nonparametric analyses in reliability currently form an interesting area of study that has not yet been fully explored. Applied Nonparametric Statistics in Reliability is focused on the use of modern statistical methods for the estimation of dependability measures of reliability systems that operate under different conditions. The scope of the book includes: smooth estimation of the reliability function and hazard rate of non-repairable systems; study of stochastic processes for modelling the time evolution of systems when imperfect repairs are performed; nonparametric analysis of discrete and continuous time semi-Markov processes; isotonic regression analysis of the structure function of a reliability system, and lifetime regression analysis. Besides the explanation of the mathematical background, several numerical computations or simulations are presented as illustrative examples. The corresponding computer-based methods have been implemented using R and MATLAB®. A concrete modelling scheme is chosen for each practical situation and, in consequence, a nonparametric inference procedure is conducted. Applied Nonparametric Statistics in Reliability will serve the practical needs of scientists (statisticians and engineers) working on applied reliability subjects.

Advances in Degradation Modeling

Author : M.S. Nikulin
Publisher : Springer Science & Business Media
ISBN 13 : 0817649247
Total Pages : 436 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Advances in Degradation Modeling by : M.S. Nikulin

Download or read book Advances in Degradation Modeling written by M.S. Nikulin and published by Springer Science & Business Media. This book was released on 2010-07-08 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of invited chapters covering recent advances in accelerated life testing and degradation models. The book covers a wide range of applications to areas such as reliability, quality control, the health sciences, economics and finance. It is an excellent reference for researchers and practitioners in applied probability and statistics, industrial statistics, the health sciences, quality control, economics, and finance.

Stochastic Processes in Cell Biology

Author : Paul C. Bressloff
Publisher : Springer Nature
ISBN 13 : 3030725154
Total Pages : 773 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Stochastic Processes in Cell Biology by : Paul C. Bressloff

Download or read book Stochastic Processes in Cell Biology written by Paul C. Bressloff and published by Springer Nature. This book was released on 2022-01-04 with total page 773 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops the theory of continuous and discrete stochastic processes within the context of cell biology. In the second edition the material has been significantly expanded, particularly within the context of nonequilibrium and self-organizing systems. Given the amount of additional material, the book has been divided into two volumes, with volume I mainly covering molecular processes and volume II focusing on cellular processes. A wide range of biological topics are covered in the new edition, including stochastic ion channels and excitable systems, molecular motors, stochastic gene networks, genetic switches and oscillators, epigenetics, normal and anomalous diffusion in complex cellular environments, stochastically-gated diffusion, active intracellular transport, signal transduction, cell sensing, bacterial chemotaxis, intracellular pattern formation, cell polarization, cell mechanics, biological polymers and membranes, nuclear structure and dynamics, biological condensates, molecular aggregation and nucleation, cellular length control, cell mitosis, cell motility, cell adhesion, cytoneme-based morphogenesis, bacterial growth, and quorum sensing. The book also provides a pedagogical introduction to the theory of stochastic and nonequilibrium processes – Fokker Planck equations, stochastic differential equations, stochastic calculus, master equations and jump Markov processes, birth-death processes, Poisson processes, first passage time problems, stochastic hybrid systems, queuing and renewal theory, narrow capture and escape, extreme statistics, search processes and stochastic resetting, exclusion processes, WKB methods, large deviation theory, path integrals, martingales and branching processes, numerical methods, linear response theory, phase separation, fluctuation-dissipation theorems, age-structured models, and statistical field theory. This text is primarily aimed at graduate students and researchers working in mathematical biology, statistical and biological physicists, and applied mathematicians interested in stochastic modeling. Applied probabilists should also find it of interest. It provides significant background material in applied mathematics and statistical physics, and introduces concepts in stochastic and nonequilibrium processes via motivating biological applications. The book is highly illustrated and contains a large number of examples and exercises that further develop the models and ideas in the body of the text. It is based on a course that the author has taught at the University of Utah for many years.

Discrete-Time Markov Control Processes

Author : Onesimo Hernandez-Lerma
Publisher : Springer Science & Business Media
ISBN 13 : 1461207290
Total Pages : 223 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Discrete-Time Markov Control Processes by : Onesimo Hernandez-Lerma

Download or read book Discrete-Time Markov Control Processes written by Onesimo Hernandez-Lerma and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the first part of a planned two-volume series devoted to a systematic exposition of some recent developments in the theory of discrete-time Markov control processes (MCPs). Interest is mainly confined to MCPs with Borel state and control (or action) spaces, and possibly unbounded costs and noncompact control constraint sets. MCPs are a class of stochastic control problems, also known as Markov decision processes, controlled Markov processes, or stochastic dynamic pro grams; sometimes, particularly when the state space is a countable set, they are also called Markov decision (or controlled Markov) chains. Regardless of the name used, MCPs appear in many fields, for example, engineering, economics, operations research, statistics, renewable and nonrenewable re source management, (control of) epidemics, etc. However, most of the lit erature (say, at least 90%) is concentrated on MCPs for which (a) the state space is a countable set, and/or (b) the costs-per-stage are bounded, and/or (c) the control constraint sets are compact. But curiously enough, the most widely used control model in engineering and economics--namely the LQ (Linear system/Quadratic cost) model-satisfies none of these conditions. Moreover, when dealing with "partially observable" systems) a standard approach is to transform them into equivalent "completely observable" sys tems in a larger state space (in fact, a space of probability measures), which is uncountable even if the original state process is finite-valued.

Asymptotic and Analytic Methods in Stochastic Evolutionary Symptoms

Author : Dmitri Koroliouk
Publisher : John Wiley & Sons
ISBN 13 : 1786309114
Total Pages : 276 pages
Book Rating : 4.7/5 (863 download)

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Book Synopsis Asymptotic and Analytic Methods in Stochastic Evolutionary Symptoms by : Dmitri Koroliouk

Download or read book Asymptotic and Analytic Methods in Stochastic Evolutionary Symptoms written by Dmitri Koroliouk and published by John Wiley & Sons. This book was released on 2023-08-29 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book illustrates a number of asymptotic and analytic approaches applied for the study of random evolutionary systems, and considers typical problems for specific examples. In this case, constructive mathematical models of natural processes are used, which more realistically describe the trajectories of diffusion-type processes, rather than those of the Wiener process. We examine models where particles have some free distance between two consecutive collisions. At the same time, we investigate two cases: the Markov evolutionary system, where the time during which the particle moves towards some direction is distributed exponentially with intensity parameter λ; and the semi-Markov evolutionary system, with arbitrary distribution of the switching process. Thus, the models investigated here describe the motion of particles with a finite speed and the proposed random evolutionary process with characteristics of a natural physical process: free run and finite propagation speed. In the proposed models, the number of possible directions of evolution can be finite or infinite.

Passage Times for Markov Chains

Author : R. Syski
Publisher : IOS Press
ISBN 13 : 9789051990607
Total Pages : 564 pages
Book Rating : 4.9/5 (96 download)

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Book Synopsis Passage Times for Markov Chains by : R. Syski

Download or read book Passage Times for Markov Chains written by R. Syski and published by IOS Press. This book was released on 1992 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a survey of work on passage times in stable Markov chains with a discrete state space and a continuous time. Passage times have been investigated since early days of probability theory and its applications. The best known example is the first entrance time to a set, which embraces waiting times, busy periods, absorption problems, extinction phenomena, etc. Another example of great interest is the last exit time from a set. The book presents a unifying treatment of passage times, written in a systematic manner and based on modern developments. The appropriate unifying framework is provided by probabilistic potential theory, and the results presented in the text are interpreted from this point of view. In particular, the crucial role of the Dirichlet problem and the Poisson equation is stressed. The work is addressed to applied probalilists, and to those who are interested in applications of probabilistic methods in their own areas of interest. The level of presentation is that of a graduate text in applied stochastic processes. Hence, clarity of presentation takes precedence over secondary mathematical details whenever no serious harm may be expected. Advanced concepts described in the text gain nowadays growing acceptance in applied fields, and it is hoped that this work will serve as an useful introduction. Abstracted by Mathematical Reviews, issue 94c