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Markov Processes From K Itos Perspective
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Book Synopsis Markov Processes from K. Itô's Perspective (AM-155) by : Daniel W. Stroock
Download or read book Markov Processes from K. Itô's Perspective (AM-155) written by Daniel W. Stroock and published by Princeton University Press. This book was released on 2003-05-06 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kiyosi Itô's greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the Kolmogorov-Feller theory of Markov processes. Starting with the geometric ideas that guided him, this book gives an account of Itô's program. The modern theory of Markov processes was initiated by A. N. Kolmogorov. However, Kolmogorov's approach was too analytic to reveal the probabilistic foundations on which it rests. In particular, it hides the central role played by the simplest Markov processes: those with independent, identically distributed increments. To remedy this defect, Itô interpreted Kolmogorov's famous forward equation as an equation that describes the integral curve of a vector field on the space of probability measures. Thus, in order to show how Itô's thinking leads to his theory of stochastic integral equations, Stroock begins with an account of integral curves on the space of probability measures and then arrives at stochastic integral equations when he moves to a pathspace setting. In the first half of the book, everything is done in the context of general independent increment processes and without explicit use of Itô's stochastic integral calculus. In the second half, the author provides a systematic development of Itô's theory of stochastic integration: first for Brownian motion and then for continuous martingales. The final chapter presents Stratonovich's variation on Itô's theme and ends with an application to the characterization of the paths on which a diffusion is supported. The book should be accessible to readers who have mastered the essentials of modern probability theory and should provide such readers with a reasonably thorough introduction to continuous-time, stochastic processes.
Book Synopsis Markov Processes from K. Itô's Perspective by : Daniel W. Stroock
Download or read book Markov Processes from K. Itô's Perspective written by Daniel W. Stroock and published by Princeton University Press. This book was released on 2003-05-26 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kiyosi Itô's greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the Kolmogorov-Feller theory of Markov processes. Starting with the geometric ideas that guided him, this book gives an account of Itô's program. The modern theory of Markov processes was initiated by A. N. Kolmogorov. However, Kolmogorov's approach was too analytic to reveal the probabilistic foundations on which it rests. In particular, it hides the central role played by the simplest Markov processes: those with independent, identically distributed increments. To remedy this defect, Itô interpreted Kolmogorov's famous forward equation as an equation that describes the integral curve of a vector field on the space of probability measures. Thus, in order to show how Itô's thinking leads to his theory of stochastic integral equations, Stroock begins with an account of integral curves on the space of probability measures and then arrives at stochastic integral equations when he moves to a pathspace setting. In the first half of the book, everything is done in the context of general independent increment processes and without explicit use of Itô's stochastic integral calculus. In the second half, the author provides a systematic development of Itô's theory of stochastic integration: first for Brownian motion and then for continuous martingales. The final chapter presents Stratonovich's variation on Itô's theme and ends with an application to the characterization of the paths on which a diffusion is supported. The book should be accessible to readers who have mastered the essentials of modern probability theory and should provide such readers with a reasonably thorough introduction to continuous-time, stochastic processes.
Book Synopsis Nonlinear Markov Processes and Kinetic Equations by : Vassili N. Kolokoltsov
Download or read book Nonlinear Markov Processes and Kinetic Equations written by Vassili N. Kolokoltsov and published by Cambridge University Press. This book was released on 2010-07-15 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: A nonlinear Markov evolution is a dynamical system generated by a measure-valued ordinary differential equation with the specific feature of preserving positivity. This feature distinguishes it from general vector-valued differential equations and yields a natural link with probability, both in interpreting results and in the tools of analysis. This brilliant book, the first devoted to the area, develops this interplay between probability and analysis. After systematically presenting both analytic and probabilistic techniques, the author uses probability to obtain deeper insight into nonlinear dynamics, and analysis to tackle difficult problems in the description of random and chaotic behavior. The book addresses the most fundamental questions in the theory of nonlinear Markov processes: existence, uniqueness, constructions, approximation schemes, regularity, law of large numbers and probabilistic interpretations. Its careful exposition makes the book accessible to researchers and graduate students in stochastic and functional analysis with applications to mathematical physics and systems biology.
Book Synopsis Introduction to Stochastic Calculus with Applications by : Fima C. Klebaner
Download or read book Introduction to Stochastic Calculus with Applications written by Fima C. Klebaner and published by Imperial College Press. This book was released on 2005 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author.
Book Synopsis Introduction to Stochastic Models by : Roe Goodman
Download or read book Introduction to Stochastic Models written by Roe Goodman and published by Courier Corporation. This book was released on 2006-01-01 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Newly revised by the author, this undergraduate-level text introduces the mathematical theory of probability and stochastic processes. Using both computer simulations and mathematical models of random events, it comprises numerous applications to the physical and biological sciences, engineering, and computer science. Subjects include sample spaces, probabilities distributions and expectations of random variables, conditional expectations, Markov chains, and the Poisson process. Additional topics encompass continuous-time stochastic processes, birth and death processes, steady-state probabilities, general queuing systems, and renewal processes. Each section features worked examples, and exercises appear at the end of each chapter, with numerical solutions at the back of the book. Suggestions for further reading in stochastic processes, simulation, and various applications also appear at the end.
Book Synopsis Mathematics and Life Sciences by : Alexandra V. Antoniouk
Download or read book Mathematics and Life Sciences written by Alexandra V. Antoniouk and published by Walter de Gruyter. This book was released on 2012-12-19 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a unique collection of in-depth mathematical, statistical, and modeling methods and techniques for life sciences, as well as their applications in a number of areas within life sciences. The book provides also with a range of new ideas that represent emerging frontiers in life sciences where the application of such quantitative methods and techniques is becoming increasingly important. Many areas within life sciences are becoming increasingly quantitative and the progress in those areas will be more and more dependent on the successful development of advanced mathematical, statistical and modelling methodologies and techniques. The state-of-the-art developments in such methodologies and techniques are scattered throughout research journals and hardly accessible to the practitioners in those areas. This book identifies a number of frontier areas where such methodologies and techniques have recently been developed and are to be published here for the first time, bringing substantial potential benefit to a range of applications in life sciences. In addition, the book contains several state-of-the-art surveys at the interface of mathematics and life sciences that would benefit a larger interdisciplinary community. It is aimed at researchers in academia, practitioners and graduate students who want to foster interdisciplinary collaborations required to meet the challenges at the interface of modern life sciences and mathematics.
Download or read book Kolmogorov in Perspective written by and published by American Mathematical Soc.. This book was released on 2000 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: The editorial board for the History of Mathematics series has selected for this volume a series of translations from two Russian publications, Kolmogorov in Remembrance and Mathematics and its Historical Development. This book, Kolmogorov in Perspective, includes articles written by Kolmogorov's students and colleagues and his personal accounts of shared experiences and lifelong mathematical friendships. The articles combine to give an excellent personal and scientific biography of this important mathematician. There is also an extensive bibliography with the complete list of Kolmogorov's work.
Book Synopsis Stochastic Analysis 2010 by : Dan Crisan
Download or read book Stochastic Analysis 2010 written by Dan Crisan and published by Springer Science & Business Media. This book was released on 2010-11-26 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Analysis aims to provide mathematical tools to describe and model high dimensional random systems. Such tools arise in the study of Stochastic Differential Equations and Stochastic Partial Differential Equations, Infinite Dimensional Stochastic Geometry, Random Media and Interacting Particle Systems, Super-processes, Stochastic Filtering, Mathematical Finance, etc. Stochastic Analysis has emerged as a core area of late 20th century Mathematics and is currently undergoing a rapid scientific development. The special volume “Stochastic Analysis 2010” provides a sample of the current research in the different branches of the subject. It includes the collected works of the participants at the Stochastic Analysis section of the 7th ISAAC Congress organized at Imperial College London in July 2009.
Author :Jean-Dominique Deuschel Publisher :Springer Science & Business Media ISBN 13 :3540271104 Total Pages :443 pages Book Rating :4.5/5 (42 download)
Book Synopsis Interacting Stochastic Systems by : Jean-Dominique Deuschel
Download or read book Interacting Stochastic Systems written by Jean-Dominique Deuschel and published by Springer Science & Business Media. This book was released on 2005-12-05 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: Core papers emanating from the research network, DFG-Schwerpunkt: Interacting stochastic systems of high complexity.
Book Synopsis The Theoretical Biologist's Toolbox by : Marc Mangel
Download or read book The Theoretical Biologist's Toolbox written by Marc Mangel and published by Cambridge University Press. This book was released on 2006-07-27 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical modelling is widely used in ecology and evolutionary biology and it is a topic that many biologists find difficult to grasp. In this new textbook Marc Mangel provides a no-nonsense introduction to the skills needed to understand the principles of theoretical and mathematical biology. Fundamental theories and applications are introduced using numerous examples from current biological research, complete with illustrations to highlight key points. Exercises are also included throughout the text to show how theory can be applied and to test knowledge gained so far. Suitable for advanced undergraduate courses in theoretical and mathematical biology, this book forms an essential resource for anyone wanting to gain an understanding of theoretical ecology and evolution.
Book Synopsis Markov Chains and Stochastic Stability by : Sean Meyn
Download or read book Markov Chains and Stochastic Stability written by Sean Meyn and published by Cambridge University Press. This book was released on 2009-04-02 with total page 623 pages. Available in PDF, EPUB and Kindle. Book excerpt: New up-to-date edition of this influential classic on Markov chains in general state spaces. Proofs are rigorous and concise, the range of applications is broad and knowledgeable, and key ideas are accessible to practitioners with limited mathematical background. New commentary by Sean Meyn, including updated references, reflects developments since 1996.
Book Synopsis Chaotic Systems by : Christos H. Skiadas
Download or read book Chaotic Systems written by Christos H. Skiadas and published by World Scientific. This book was released on 2010 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of papers suggested by the Scientific Committee that includes the best papers presented in the 2nd International Conference (CHAOS2009) on Chaotic Modeling, Simulation and Applications, that was held in Chania, Crete, Greece, June 1-5, 2009. The aim of the conference was to invite and bring together people working in interesting topics of chaotic modeling, nonlinear and dynamical systems and chaotic simulation. The volume presents theoretical and applied contributions on chaotic systems. Papers from several nonlinear analysis and chaotic fields are included and new and very important results are presented. Emphasis was given to the selection of works that have significant impact in the chaotic field and open new horizons to further develop related topics and subjects. Even more the selected papers are addressed to an interdisciplinary audience aiming at the broad dissemination of the theory and practice of chaotic modeling and simulation and nonlinear science.
Book Synopsis Mathematical Methods for Financial Markets by : Monique Jeanblanc
Download or read book Mathematical Methods for Financial Markets written by Monique Jeanblanc and published by Springer Science & Business Media. This book was released on 2009-10-03 with total page 754 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical finance has grown into a huge area of research which requires a large number of sophisticated mathematical tools. This book simultaneously introduces the financial methodology and the relevant mathematical tools in a style that is mathematically rigorous and yet accessible to practitioners and mathematicians alike. It interlaces financial concepts such as arbitrage opportunities, admissible strategies, contingent claims, option pricing and default risk with the mathematical theory of Brownian motion, diffusion processes, and Lévy processes. The first half of the book is devoted to continuous path processes whereas the second half deals with discontinuous processes. The extensive bibliography comprises a wealth of important references and the author index enables readers quickly to locate where the reference is cited within the book, making this volume an invaluable tool both for students and for those at the forefront of research and practice.
Book Synopsis Lectures from Markov Processes to Brownian Motion by : Kai Lai Chung
Download or read book Lectures from Markov Processes to Brownian Motion written by Kai Lai Chung and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book evolved from several stacks of lecture notes written over a decade and given in classes at slightly varying levels. In transforming the over lapping material into a book, I aimed at presenting some of the best features of the subject with a minimum of prerequisities and technicalities. (Needless to say, one man's technicality is another's professionalism. ) But a text frozen in print does not allow for the latitude of the classroom; and the tendency to expand becomes harder to curb without the constraints of time and audience. The result is that this volume contains more topics and details than I had intended, but I hope the forest is still visible with the trees. The book begins at the beginning with the Markov property, followed quickly by the introduction of option al times and martingales. These three topics in the discrete parameter setting are fully discussed in my book A Course In Probability Theory (second edition, Academic Press, 1974). The latter will be referred to throughout this book as the Course, and may be considered as a general background; its specific use is limited to the mate rial on discrete parameter martingale theory cited in § 1. 4. Apart from this and some dispensable references to Markov chains as examples, the book is self-contained.
Book Synopsis Bit-string Physics: A Finite & Discrete Approach To Natural Philosophy by : Henry Pierre Noyes
Download or read book Bit-string Physics: A Finite & Discrete Approach To Natural Philosophy written by Henry Pierre Noyes and published by World Scientific. This book was released on 2001-09-06 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: We could be on the threshold of a scientific revolution. Quantum mechanics is based on unique, finite, and discrete events. General relativity assumes a continuous, curved space-time. Reconciling the two remains the most fundamental unsolved scientific problem left over from the last century. The papers of H Pierre Noyes collected in this volume reflect one attempt to achieve that unification by replacing the continuum with the bit-string events of computer science. Three principles are used: physics can determine whether two quantities are the same or different; measurement can tell something from nothing; this structure (modeled by binary addition and multiplication) can leave a historical record consisting of a growing universe of bit-strings. This book is specifically addressed to those interested in the foundations of particle physics, relativity, quantum mechanics, physical cosmology and the philosophy of science.
Book Synopsis Stochastic Partial Differential Equations: Six Perspectives by : René Carmona
Download or read book Stochastic Partial Differential Equations: Six Perspectives written by René Carmona and published by American Mathematical Soc.. This book was released on 1999 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the main topics of interest in the field of stochastic partial differential equations (SPDEs), emphasizing breakthroughs and such basic issues as the role of SPDEs in stochastic modeling, how SPDEs arise, and how their theory is applied in different disciplines. Emphasis is placed on the genesis and applications of SPDEs, as well as mathematical theory and numerical methods. Suitable for graduate level students, researchers. Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis Computation and Applied Mathematics by :
Download or read book Computation and Applied Mathematics written by and published by . This book was released on 1997 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:
