Path Properties Of Rare Events

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Path Properties of Rare Events

Author : Jesse Collingwood
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (97 download)

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Book Synopsis Path Properties of Rare Events by : Jesse Collingwood

Download or read book Path Properties of Rare Events written by Jesse Collingwood and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Simulation of rare events can be costly with respect to time and computational resources. For certain processes it may be more efficient to begin at the rare event and simulate a kind of reversal of the process. This approach is particularly well suited to reversible Markov processes, but holds much more generally. This more general result is formulated precisely in the language of stationary point processes, proven, and applied to some examples. An interesting question is whether this technique can be applied to Markov processes which are substochastic, i.e. processes which may die if a graveyard state is ever reached. First, some of the theory of substochastic processes is developed; in particular a slightly surprising result about the rate of convergence of the distribution pi(n) at time n of the process conditioned to stay alive to the quasi-stationary distribution, or Yaglom limit, is proved. This result is then verified with some illustrative examples. Next, it is demonstrated with an explicit example that on infinite state spaces the reversal approach to analyzing both the rate of convergence to the Yaglom limit and the likely path of rare events can fail due to transience.

Reaction Rate Theory and Rare Events

Author : Baron Peters
Publisher : Elsevier
ISBN 13 : 0444594701
Total Pages : 636 pages
Book Rating : 4.4/5 (445 download)

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Book Synopsis Reaction Rate Theory and Rare Events by : Baron Peters

Download or read book Reaction Rate Theory and Rare Events written by Baron Peters and published by Elsevier. This book was released on 2017-03-22 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reaction Rate Theory and Rare Events bridges the historical gap between these subjects because the increasingly multidisciplinary nature of scientific research often requires an understanding of both reaction rate theory and the theory of other rare events. The book discusses collision theory, transition state theory, RRKM theory, catalysis, diffusion limited kinetics, mean first passage times, Kramers theory, Grote-Hynes theory, transition path theory, non-adiabatic reactions, electron transfer, and topics from reaction network analysis. It is an essential reference for students, professors and scientists who use reaction rate theory or the theory of rare events. In addition, the book discusses transition state search algorithms, tunneling corrections, transmission coefficients, microkinetic models, kinetic Monte Carlo, transition path sampling, and importance sampling methods. The unified treatment in this book explains why chemical reactions and other rare events, while having many common theoretical foundations, often require very different computational modeling strategies. Offers an integrated approach to all simulation theories and reaction network analysis, a unique approach not found elsewhere Gives algorithms in pseudocode for using molecular simulation and computational chemistry methods in studies of rare events Uses graphics and explicit examples to explain concepts Includes problem sets developed and tested in a course range from pen-and-paper theoretical problems, to computational exercises

Rare Event Simulation using Monte Carlo Methods

Author : Gerardo Rubino
Publisher : John Wiley & Sons
ISBN 13 : 9780470745410
Total Pages : 278 pages
Book Rating : 4.7/5 (454 download)

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Book Synopsis Rare Event Simulation using Monte Carlo Methods by : Gerardo Rubino

Download or read book Rare Event Simulation using Monte Carlo Methods written by Gerardo Rubino and published by John Wiley & Sons. This book was released on 2009-03-18 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a probabilistic model, a rare event is an event with a very small probability of occurrence. The forecasting of rare events is a formidable task but is important in many areas. For instance a catastrophic failure in a transport system or in a nuclear power plant, the failure of an information processing system in a bank, or in the communication network of a group of banks, leading to financial losses. Being able to evaluate the probability of rare events is therefore a critical issue. Monte Carlo Methods, the simulation of corresponding models, are used to analyze rare events. This book sets out to present the mathematical tools available for the efficient simulation of rare events. Importance sampling and splitting are presented along with an exposition of how to apply these tools to a variety of fields ranging from performance and dependability evaluation of complex systems, typically in computer science or in telecommunications, to chemical reaction analysis in biology or particle transport in physics. Graduate students, researchers and practitioners who wish to learn and apply rare event simulation techniques will find this book beneficial.

Introduction to Rare Event Simulation

Author : James Bucklew
Publisher : Springer Science & Business Media
ISBN 13 : 1475740786
Total Pages : 262 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Introduction to Rare Event Simulation by : James Bucklew

Download or read book Introduction to Rare Event Simulation written by James Bucklew and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unified theory of rare event simulation and the variance reduction technique known as importance sampling from the point of view of the probabilistic theory of large deviations. It allows us to view a vast assortment of simulation problems from a unified single perspective.

Advances in Chemical Physics

Author : Ilya Prigogine
Publisher : John Wiley & Sons
ISBN 13 : 0471461490
Total Pages : 696 pages
Book Rating : 4.4/5 (714 download)

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Book Synopsis Advances in Chemical Physics by : Ilya Prigogine

Download or read book Advances in Chemical Physics written by Ilya Prigogine and published by John Wiley & Sons. This book was released on 2003-04-14 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: The latest edition of the leading forum in chemical physics Edited by Nobel Prize winner Ilya Prigogine and renowned authority Stuart A. Rice. The Advances in Chemical Physics series provides a forum for critical, authoritative evaluations in every area of the discipline. In a format that encourages the expression of individual points of view, experts in the field present comprehensive analyses of subjects of interest. This stand-alone, special topics volume reports recent advances in electron-transfer research, with significant, up-to-date chapters by internationally recognized researchers. Volume 123 collects innovative papers on "Transition Path Sampling," "Dynamics of Chemical Reactions and Chaos," "The Role of Self Similarity in Renormalization Group Theory," and several other related topics. Advances in Chemical Physics remains the premier venue for presentations of new findings in its field.

Probability Approximations via the Poisson Clumping Heuristic

Author : David Aldous
Publisher : Springer Science & Business Media
ISBN 13 : 1475762836
Total Pages : 285 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Probability Approximations via the Poisson Clumping Heuristic by : David Aldous

Download or read book Probability Approximations via the Poisson Clumping Heuristic written by David Aldous and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: If you place a large number of points randomly in the unit square, what is the distribution of the radius of the largest circle containing no points? Of the smallest circle containing 4 points? Why do Brownian sample paths have local maxima but not points of increase, and how nearly do they have points of increase? Given two long strings of letters drawn i. i. d. from a finite alphabet, how long is the longest consecutive (resp. non-consecutive) substring appearing in both strings? If an imaginary particle performs a simple random walk on the vertices of a high-dimensional cube, how long does it take to visit every vertex? If a particle moves under the influence of a potential field and random perturbations of velocity, how long does it take to escape from a deep potential well? If cars on a freeway move with constant speed (random from car to car), what is the longest stretch of empty road you will see during a long journey? If you take a large i. i. d. sample from a 2-dimensional rotationally-invariant distribution, what is the maximum over all half-spaces of the deviation between the empirical and true distributions? These questions cover a wide cross-section of theoretical and applied probability. The common theme is that they all deal with maxima or min ima, in some sense.

Formal Methods

Author : Klaus Havelund
Publisher : Springer
ISBN 13 : 3319955829
Total Pages : 702 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Formal Methods by : Klaus Havelund

Download or read book Formal Methods written by Klaus Havelund and published by Springer. This book was released on 2018-07-11 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 22nd International Symposium on Formal Methods, FM 2018, held in Oxford, UK, in July 2018. The 44 full papers presented together with 2 invited papers were carefully reviewed and selected from 110 submissions. They present formal methods for developing and evaluating systems. Examples include autonomous systems, robots, and cyber-physical systems in general. The papers cover a broad range of topics in the following areas: interdisciplinary formal methods; formal methods in practice; tools for formal methods; role of formal methods in software systems engineering; and theoretical foundations.

An Introduction to the Mathematics of Financial Derivatives

Author : Ali Hirsa
Publisher : Academic Press
ISBN 13 : 0123846838
Total Pages : 456 pages
Book Rating : 4.1/5 (238 download)

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Book Synopsis An Introduction to the Mathematics of Financial Derivatives by : Ali Hirsa

Download or read book An Introduction to the Mathematics of Financial Derivatives written by Ali Hirsa and published by Academic Press. This book was released on 2013-12-18 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to the Mathematics of Financial Derivatives is a popular, intuitive text that eases the transition between basic summaries of financial engineering to more advanced treatments using stochastic calculus. Requiring only a basic knowledge of calculus and probability, it takes readers on a tour of advanced financial engineering. This classic title has been revised by Ali Hirsa, who accentuates its well-known strengths while introducing new subjects, updating others, and bringing new continuity to the whole. Popular with readers because it emphasizes intuition and common sense, An Introduction to the Mathematics of Financial Derivatives remains the only "introductory" text that can appeal to people outside the mathematics and physics communities as it explains the hows and whys of practical finance problems. Facilitates readers' understanding of underlying mathematical and theoretical models by presenting a mixture of theory and applications with hands-on learning Presented intuitively, breaking up complex mathematics concepts into easily understood notions Encourages use of discrete chapters as complementary readings on different topics, offering flexibility in learning and teaching

Efficient Control and Spontaneous Transitions

Author : Miranda Louwerse
Publisher : Springer Nature
ISBN 13 : 303140534X
Total Pages : 123 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Efficient Control and Spontaneous Transitions by : Miranda Louwerse

Download or read book Efficient Control and Spontaneous Transitions written by Miranda Louwerse and published by Springer Nature. This book was released on 2023-12-02 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis addresses deep questions that cut to the physical and informational essence of central chemical quantities such as transition paths and reaction mechanisms and proposes fundamental new connections between transition-path theory, linear-response theory, nonequilibrium thermodynamics, and information theory. The author investigates slow, energetically efficient driving protocols that drive a system between conformations corresponding to endpoints of a reaction, aiming to find connections between principles of efficient driving and the spontaneous transition mechanism in the absence of driving. First, an alternative perspective of transition-path theory is developed that unifies it with stochastic thermodynamics to describe flows of entropy, energy, and information during the reaction. This also provides an optimization criterion for selecting collective variables. Next, protocols are designed which invert the magnetization of a 3×3 Ising model with minimal energetic cost, and it is determined that using multiple control parameters allows the system to be driven along a fast-relaxing pathway between reaction endpoints. Finally, the author compares these protocols with the spontaneous transition mechanism for magnetization inversion in the same Ising model, finding that designed protocols capture general features of the spontaneous mechanism and energetics given the constraints on the control parameters. This work represents a major step forward in our understanding of rare events and provides a basis for investigating the connection between efficient protocols and spontaneous transition mechanisms which can be further probed in a wider variety of systems.

Model Checking Software

Author : Georgiana Caltais
Publisher : Springer Nature
ISBN 13 : 303132157X
Total Pages : 202 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Model Checking Software by : Georgiana Caltais

Download or read book Model Checking Software written by Georgiana Caltais and published by Springer Nature. This book was released on 2023-05-01 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 29th International Symposium on Model Checking Software, SPIN 2023, held in Paris, France, during April 26–27, 2023. The 9 full papers and 2 short papers included in this book were carefully reviewed and selected from 21 submissions. They were organized in topical sections as follows: binary decision diagrams, concurrency, testing, synthesis, explicit-state model checking.

An Introduction to the Mathematics of Financial Derivatives

Author : Salih N. Neftci
Publisher : Academic Press
ISBN 13 : 0125153929
Total Pages : 550 pages
Book Rating : 4.1/5 (251 download)

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Book Synopsis An Introduction to the Mathematics of Financial Derivatives by : Salih N. Neftci

Download or read book An Introduction to the Mathematics of Financial Derivatives written by Salih N. Neftci and published by Academic Press. This book was released on 2000-05-19 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: A step-by-step explanation of the mathematical models used to price derivatives. For this second edition, Salih Neftci has expanded one chapter, added six new ones, and inserted chapter-concluding exercises. He does not assume that the reader has a thorough mathematical background. His explanations of financial calculus seek to be simple and perceptive.

Analysis and Approximation of Rare Events

Author : Amarjit Budhiraja
Publisher : Springer
ISBN 13 : 1493995790
Total Pages : 574 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Analysis and Approximation of Rare Events by : Amarjit Budhiraja

Download or read book Analysis and Approximation of Rare Events written by Amarjit Budhiraja and published by Springer. This book was released on 2019-08-10 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents broadly applicable methods for the large deviation and moderate deviation analysis of discrete and continuous time stochastic systems. A feature of the book is the systematic use of variational representations for quantities of interest such as normalized logarithms of probabilities and expected values. By characterizing a large deviation principle in terms of Laplace asymptotics, one converts the proof of large deviation limits into the convergence of variational representations. These features are illustrated though their application to a broad range of discrete and continuous time models, including stochastic partial differential equations, processes with discontinuous statistics, occupancy models, and many others. The tools used in the large deviation analysis also turn out to be useful in understanding Monte Carlo schemes for the numerical approximation of the same probabilities and expected values. This connection is illustrated through the design and analysis of importance sampling and splitting schemes for rare event estimation. The book assumes a solid background in weak convergence of probability measures and stochastic analysis, and is suitable for advanced graduate students, postdocs and researchers.

Probability Theory

Author : Heinz Bauer
Publisher : Walter de Gruyter
ISBN 13 : 3110814668
Total Pages : 541 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Probability Theory by : Heinz Bauer

Download or read book Probability Theory written by Heinz Bauer and published by Walter de Gruyter. This book was released on 2011-05-03 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob. Titles in planning include Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic Models for Fractional Calculus, second edition (2018) Flavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures and Applications to Parabolic Problems (2019) Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019) Kezheng Li, Group Schemes and Their Actions (2019; together with Tsinghua University Press) Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021) Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)

Large Deviations For Performance Analysis

Author : Alan Weiss
Publisher : Routledge
ISBN 13 : 042984686X
Total Pages : 295 pages
Book Rating : 4.4/5 (298 download)

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Book Synopsis Large Deviations For Performance Analysis by : Alan Weiss

Download or read book Large Deviations For Performance Analysis written by Alan Weiss and published by Routledge. This book was released on 2019-03-07 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1995, Large Deviations for Performance Analysis consists of two synergistic parts. The first half develops the theory of large deviations from the beginning, through recent results on the theory for processes with boundaries, keeping to a very narrow path: continuous-time, discrete-state processes. By developing only what is needed for the applications, the theory is kept to a manageable level, both in terms of length and in terms of difficulty. Within its scope, the treatment is detailed, comprehensive and self-contained. As the book shows, there are sufficiently many interesting applications of jump Markov processes to warrant a special treatment. The second half is a collection of applications developed at Bell Laboratories. The applications cover large areas of the theory of communication networks: circuit switched transmission, packet transmission, multiple access channels, and the M/M/1 queue. Aspects of parallel computation are covered as well including, basics of job allocation, rollback-based parallel simulation, assorted priority queueing models that might be used in performance models of various computer architectures, and asymptotic coupling of processors. These applications are thoroughly analysed using the tools developed in the first half of the book.

An Introduction to the Analysis of Paths on a Riemannian Manifold

Author : Daniel W. Stroock
Publisher : American Mathematical Soc.
ISBN 13 : 0821838393
Total Pages : 290 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis An Introduction to the Analysis of Paths on a Riemannian Manifold by : Daniel W. Stroock

Download or read book An Introduction to the Analysis of Paths on a Riemannian Manifold written by Daniel W. Stroock and published by American Mathematical Soc.. This book was released on 2000 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hoping to make the text more accessible to readers not schooled in the probabalistic tradition, Stroock (affiliation unspecified) emphasizes the geometric over the stochastic analysis of differential manifolds. Chapters deconstruct Brownian paths, diffusions in Euclidean space, intrinsic and extrinsic Riemannian geometry, Bocher's identity, and the bundle of orthonormal frames. The volume humbly concludes with an "admission of defeat" in regard to recovering the Li-Yau basic differential inequality. Annotation copyrighted by Book News, Inc., Portland, OR.

Statistics for Spatial Data

Author : Noel Cressie
Publisher : John Wiley & Sons
ISBN 13 : 1119115183
Total Pages : 931 pages
Book Rating : 4.1/5 (191 download)

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Book Synopsis Statistics for Spatial Data by : Noel Cressie

Download or read book Statistics for Spatial Data written by Noel Cressie and published by John Wiley & Sons. This book was released on 2015-03-18 with total page 931 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Wiley Classics Library consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. Spatial statistics — analyzing spatial data through statistical models — has proven exceptionally versatile, encompassing problems ranging from the microscopic to the astronomic. However, for the scientist and engineer faced only with scattered and uneven treatments of the subject in the scientific literature, learning how to make practical use of spatial statistics in day-to-day analytical work is very difficult. Designed exclusively for scientists eager to tap into the enormous potential of this analytical tool and upgrade their range of technical skills, Statistics for Spatial Data is a comprehensive, single-source guide to both the theory and applied aspects of spatial statistical methods. The hard-cover edition was hailed by Mathematical Reviews as an "excellent book which will become a basic reference." This paper-back edition of the 1993 edition, is designed to meet the many technological challenges facing the scientist and engineer. Concentrating on the three areas of geostatistical data, lattice data, and point patterns, the book sheds light on the link between data and model, revealing how design, inference, and diagnostics are an outgrowth of that link. It then explores new methods to reveal just how spatial statistical models can be used to solve important problems in a host of areas in science and engineering. Discussion includes: Exploratory spatial data analysis Spectral theory for stationary processes Spatial scale Simulation methods for spatial processes Spatial bootstrapping Statistical image analysis and remote sensing Computational aspects of model fitting Application of models to disease mapping Designed to accommodate the practical needs of the professional, it features a unified and common notation for its subject as well as many detailed examples woven into the text, numerous illustrations (including graphs that illuminate the theory discussed) and over 1,000 references. Fully balancing theory with applications, Statistics for Spatial Data, Revised Edition is an exceptionally clear guide on making optimal use of one of the ascendant analytical tools of the decade, one that has begun to capture the imagination of professionals in biology, earth science, civil, electrical, and agricultural engineering, geography, epidemiology, and ecology.

Molecular Dynamics Simulation

Author : Giovanni Ciccotti
Publisher : MDPI
ISBN 13 : 3906980650
Total Pages : 627 pages
Book Rating : 4.9/5 (69 download)

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Book Synopsis Molecular Dynamics Simulation by : Giovanni Ciccotti

Download or read book Molecular Dynamics Simulation written by Giovanni Ciccotti and published by MDPI. This book was released on 2018-10-08 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: Printed Edition of the Special Issue Published in Entropy