Fluctuations In Markov Processes

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Fluctuations in Markov Processes

Tomasz Komorowski,Claudio Landim,Stefano Olla
Fluctuations in Markov Processes Book PDF

Author : Tomasz Komorowski,Claudio Landim,Stefano Olla
Publisher : Springer Science & Business Media
Page : 494 pages
File Size : 51,5 Mb
Release : 2012-07-05
Category : Mathematics
ISBN : 9783642298806

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Fluctuations in Markov Processes by Tomasz Komorowski,Claudio Landim,Stefano Olla Pdf

The present volume contains the most advanced theories on the martingale approach to central limit theorems. Using the time symmetry properties of the Markov processes, the book develops the techniques that allow us to deal with infinite dimensional models that appear in statistical mechanics and engineering (interacting particle systems, homogenization in random environments, and diffusion in turbulent flows, to mention just a few applications). The first part contains a detailed exposition of the method, and can be used as a text for graduate courses. The second concerns application to exclusion processes, in which the duality methods are fully exploited. The third part is about the homogenization of diffusions in random fields, including passive tracers in turbulent flows (including the superdiffusive behavior). There are no other books in the mathematical literature that deal with this kind of approach to the problem of the central limit theorem. Hence, this volume meets the demand for a monograph on this powerful approach, now widely used in many areas of probability and mathematical physics. The book also covers the connections with and application to hydrodynamic limits and homogenization theory, so besides probability researchers it will also be of interest also to mathematical physicists and analysts.

Markov Processes

Daniel T. Gillespie
Markov Processes Book PDF

Author : Daniel T. Gillespie
Publisher : Elsevier
Page : 590 pages
File Size : 44,6 Mb
Release : 1991-12-02
Category : Mathematics
ISBN : 9780080918372

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Markov Processes by Daniel T. Gillespie Pdf

Markov process theory is basically an extension of ordinary calculus to accommodate functions whos time evolutions are not entirely deterministic. It is a subject that is becoming increasingly important for many fields of science. This book develops the single-variable theory of both continuous and jump Markov processes in a way that should appeal especially to physicists and chemists at the senior and graduate level. A self-contained, prgamatic exposition of the needed elements of random variable theory Logically integrated derviations of the Chapman-Kolmogorov equation, the Kramers-Moyal equations, the Fokker-Planck equations, the Langevin equation, the master equations, and the moment equations Detailed exposition of Monte Carlo simulation methods, with plots of many numerical examples Clear treatments of first passages, first exits, and stable state fluctuations and transitions Carefully drawn applications to Brownian motion, molecular diffusion, and chemical kinetics

Fluctuation Theory for Lévy Processes

Ronald A. Doney
Fluctuation Theory for L vy Processes Book PDF

Author : Ronald A. Doney
Publisher : École d'Été de Probabilités de Saint-Flour
Page : 168 pages
File Size : 54,8 Mb
Release : 2007-04-19
Category : Mathematics
ISBN : UVA:X030236690

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Fluctuation Theory for Lévy Processes by Ronald A. Doney Pdf

Lévy processes, i.e. processes in continuous time with stationary and independent increments, are named after Paul Lévy, who made the connection with infinitely divisible distributions and described their structure. They form a flexible class of models, which have been applied to the study of storage processes, insurance risk, queues, turbulence, laser cooling, ... and of course finance, where the feature that they include examples having "heavy tails" is particularly important. Their sample path behaviour poses a variety of difficult and fascinating problems. Such problems, and also some related distributional problems, are addressed in detail in these notes that reflect the content of the course given by R. Doney in St. Flour in 2005.

Elements of the Theory of Markov Processes and Their Applications

A. T. Bharucha-Reid
Elements of the Theory of Markov Processes and Their Applications Book PDF

Author : A. T. Bharucha-Reid
Publisher : Courier Corporation
Page : 485 pages
File Size : 49,9 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486150352

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Elements of the Theory of Markov Processes and Their Applications by A. T. Bharucha-Reid Pdf

This graduate-level text and reference in probability, with numerous applications to several fields of science, presents nonmeasure-theoretic introduction to theory of Markov processes. The work also covers mathematical models based on the theory, employed in various applied fields. Prerequisites are a knowledge of elementary probability theory, mathematical statistics, and analysis. Appendixes. Bibliographies. 1960 edition.

Fluctuations of Lévy Processes with Applications

Andreas E. Kyprianou
Fluctuations of L vy Processes with Applications Book PDF

Author : Andreas E. Kyprianou
Publisher : Springer Science & Business Media
Page : 461 pages
File Size : 43,6 Mb
Release : 2014-01-09
Category : Mathematics
ISBN : 9783642376320

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Fluctuations of Lévy Processes with Applications by Andreas E. Kyprianou Pdf

Lévy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their application appears in the theory of many areas of classical and modern stochastic processes including storage models, renewal processes, insurance risk models, optimal stopping problems, mathematical finance, continuous-state branching processes and positive self-similar Markov processes. This textbook is based on a series of graduate courses concerning the theory and application of Lévy processes from the perspective of their path fluctuations. Central to the presentation is the decomposition of paths in terms of excursions from the running maximum as well as an understanding of short- and long-term behaviour. The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Lévy processes with jumps in only one direction, for which recent theoretical advances have yielded a higher degree of mathematical tractability. The second edition additionally addresses recent developments in the potential analysis of subordinators, Wiener-Hopf theory, the theory of scale functions and their application to ruin theory, as well as including an extensive overview of the classical and modern theory of positive self-similar Markov processes. Each chapter has a comprehensive set of exercises.

Markov Processes

Daniel T. Gillespie
Markov Processes Book PDF

Author : Daniel T. Gillespie
Publisher : Gulf Professional Publishing
Page : 600 pages
File Size : 45,9 Mb
Release : 1992
Category : Mathematics
ISBN : 0122839552

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Markov Processes by Daniel T. Gillespie Pdf

Markov process theory provides a mathematical framework for analyzing the elements of randomness that are involved in most real-world dynamical processes. This introductory text, which requires an understanding of ordinary calculus, develops the concepts and results of random variable theory.

Non-Linear Transformations of Stochastic Processes

P. I. Kuznetsov,R. L. Stratonovich,V. I. Tikhonov
Non Linear Transformations of Stochastic Processes Book PDF

Author : P. I. Kuznetsov,R. L. Stratonovich,V. I. Tikhonov
Publisher : Elsevier
Page : 514 pages
File Size : 40,6 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483282688

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Non-Linear Transformations of Stochastic Processes by P. I. Kuznetsov,R. L. Stratonovich,V. I. Tikhonov Pdf

Non-Linear Transformations of Stochastic Processes focuses on the approaches, methodologies, transformations, and computations involved in the non-linear transformations of stochastic processes. The selection first underscores some problems of the theory of stochastic processes and the transmission of random functions through non-linear systems. Discussions focus on the transformation of moment functions for the general non-linear transformation; conversion formulas for correlation functions; transformation of moment functions for the simplest type of non-linear transformation; and normalization of the linear system of probability distribution laws. The text then ponders on quasi-moment functions in the theory of random processes and correlation functions in the theory of the Brownian motion generalization of the Fokker-Planck equation. The manuscript elaborates on the correlation functions of random sequences of rectangular pulses; method of determining the envelope of quasi-harmonic fluctuations; and the problem of measuring electrical fluctuations with the aid of thermoelectric devices. The book then examines the effect of signal and noise on non-linear elements and the approximate method of calculating the correlation function of stochastic signals. The selection is a dependable source of information for researchers interested in the non-linear transformations of stochastic processes.

Nonlinear Markov Processes and Kinetic Equations

Vassili N. Kolokoltsov
Nonlinear Markov Processes and Kinetic Equations Book PDF

Author : Vassili N. Kolokoltsov
Publisher : Cambridge University Press
Page : 394 pages
File Size : 43,9 Mb
Release : 2010-07-15
Category : Mathematics
ISBN : 9781139489737

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Nonlinear Markov Processes and Kinetic Equations by Vassili N. Kolokoltsov Pdf

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.

Finite Markov Processes and Their Applications

Marius Iosifescu
Finite Markov Processes and Their Applications Book PDF

Author : Marius Iosifescu
Publisher : Courier Corporation
Page : 305 pages
File Size : 53,6 Mb
Release : 2014-07-01
Category : Mathematics
ISBN : 9780486150581

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Finite Markov Processes and Their Applications by Marius Iosifescu Pdf

A self-contained treatment of finite Markov chains and processes, this text covers both theory and applications. Author Marius Iosifescu, vice president of the Romanian Academy and director of its Center for Mathematical Statistics, begins with a review of relevant aspects of probability theory and linear algebra. Experienced readers may start with the second chapter, a treatment of fundamental concepts of homogeneous finite Markov chain theory that offers examples of applicable models. The text advances to studies of two basic types of homogeneous finite Markov chains: absorbing and ergodic chains. A complete study of the general properties of homogeneous chains follows. Succeeding chapters examine the fundamental role of homogeneous infinite Markov chains in mathematical modeling employed in the fields of psychology and genetics; the basics of nonhomogeneous finite Markov chain theory; and a study of Markovian dependence in continuous time, which constitutes an elementary introduction to the study of continuous parameter stochastic processes.

Introductory Lectures on Fluctuations of Lévy Processes with Applications

Andreas E. Kyprianou
Introductory Lectures on Fluctuations of L vy Processes with Applications Book PDF

Author : Andreas E. Kyprianou
Publisher : Springer Science & Business Media
Page : 378 pages
File Size : 41,7 Mb
Release : 2006-12-18
Category : Mathematics
ISBN : 9783540313434

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Introductory Lectures on Fluctuations of Lévy Processes with Applications by Andreas E. Kyprianou Pdf

This textbook forms the basis of a graduate course on the theory and applications of Lévy processes, from the perspective of their path fluctuations. The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Lévy processes with jumps in only one direction, for which recent theoretical advances have yielded a higher degree of mathematical transparency and explicitness.

Stochastic Processes in Physics and Chemistry

N.G. Van Kampen
Stochastic Processes in Physics and Chemistry Book PDF

Author : N.G. Van Kampen
Publisher : Elsevier
Page : 464 pages
File Size : 44,6 Mb
Release : 2011-08-30
Category : Science
ISBN : 0080475361

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Stochastic Processes in Physics and Chemistry by N.G. Van Kampen Pdf

The third edition of Van Kampen's standard work has been revised and updated. The main difference with the second edition is that the contrived application of the quantum master equation in section 6 of chapter XVII has been replaced with a satisfactory treatment of quantum fluctuations. Apart from that throughout the text corrections have been made and a number of references to later developments have been included. From the recent textbooks the following are the most relevant. C.W.Gardiner, Quantum Optics (Springer, Berlin 1991) D.T. Gillespie, Markov Processes (Academic Press, San Diego 1992) W.T. Coffey, Yu.P.Kalmykov, and J.T.Waldron, The Langevin Equation (2nd edition, World Scientific, 2004) Comprehensive coverage of fluctuations and stochastic methods for describing them A must for students and researchers in applied mathematics, physics and physical chemistry

Generated Dynamics of Markov and Quantum Processes

Martin Janßen
Generated Dynamics of Markov and Quantum Processes Book PDF

Author : Martin Janßen
Publisher : Springer
Page : 226 pages
File Size : 52,9 Mb
Release : 2016-04-28
Category : Science
ISBN : 9783662496961

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Generated Dynamics of Markov and Quantum Processes by Martin Janßen Pdf

This book presents Markov and quantum processes as two sides of a coin called generated stochastic processes. It deals with quantum processes as reversible stochastic processes generated by one-step unitary operators, while Markov processes are irreversible stochastic processes generated by one-step stochastic operators. The characteristic feature of quantum processes are oscillations, interference, lots of stationary states in bounded systems and possible asymptotic stationary scattering states in open systems, while the characteristic feature of Markov processes are relaxations to a single stationary state. Quantum processes apply to systems where all variables, that control reversibility, are taken as relevant variables, while Markov processes emerge when some of those variables cannot be followed and are thus irrelevant for the dynamic description. Their absence renders the dynamic irreversible. A further aim is to demonstrate that almost any subdiscipline of theoretical physics can conceptually be put into the context of generated stochastic processes. Classical mechanics and classical field theory are deterministic processes which emerge when fluctuations in relevant variables are negligible. Quantum mechanics and quantum field theory consider genuine quantum processes. Equilibrium and non-equilibrium statistics apply to the regime where relaxing Markov processes emerge from quantum processes by omission of a large number of uncontrollable variables. Systems with many variables often self-organize in such a way that only a few slow variables can serve as relevant variables. Symmetries and topological classes are essential in identifying such relevant variables. The third aim of this book is to provide conceptually general methods of solutions which can serve as starting points to find relevant variables as to apply best-practice approximation methods. Such methods are available through generating functionals. The potential reader is a graduate student who has heard already a course in quantum theory and equilibrium statistical physics including the mathematics of spectral analysis (eigenvalues, eigenvectors, Fourier and Laplace transformation). The reader should be open for a unifying look on several topics.

Markov Set-Chains

Darald J. Hartfiel
Markov Set Chains Book PDF

Author : Darald J. Hartfiel
Publisher : Springer
Page : 135 pages
File Size : 49,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540687115

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Markov Set-Chains by Darald J. Hartfiel Pdf

In this study extending classical Markov chain theory to handle fluctuating transition matrices, the author develops a theory of Markov set-chains and provides numerous examples showing how that theory can be applied. Chapters are concluded with a discussion of related research. Readers who can benefit from this monograph are those interested in, or involved with, systems whose data is imprecise or that fluctuate with time. A background equivalent to a course in linear algebra and one in probability theory should be sufficient.

Stochastic Processes in Physics, Chemistry, and Biology

Jan A. Freund,Thorsten Pöschel
Stochastic Processes in Physics Chemistry and Biology Book PDF

Author : Jan A. Freund,Thorsten Pöschel
Publisher : Springer Science & Business Media
Page : 512 pages
File Size : 52,5 Mb
Release : 2000-10-04
Category : Science
ISBN : 9783540410744

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Stochastic Processes in Physics, Chemistry, and Biology by Jan A. Freund,Thorsten Pöschel Pdf

The theory of stochastic processes originally grew out of efforts to describe Brownian motion quantitatively. Today it provides a huge arsenal of methods suitable for analyzing the influence of noise on a wide range of systems. The credit for acquiring all the deep insights and powerful methods is due ma- ly to a handful of physicists and mathematicians: Einstein, Smoluchowski, Langevin, Wiener, Stratonovich, etc. Hence it is no surprise that until - cently the bulk of basic and applied stochastic research was devoted to purely mathematical and physical questions. However, in the last decade we have witnessed an enormous growth of results achieved in other sciences - especially chemistry and biology - based on applying methods of stochastic processes. One reason for this stochastics boom may be that the realization that noise plays a constructive rather than the expected deteriorating role has spread to communities beyond physics. Besides their aesthetic appeal these noise-induced, noise-supported or noise-enhanced effects sometimes offer an explanation for so far open pr- lems (information transmission in the nervous system and information p- cessing in the brain, processes at the cell level, enzymatic reactions, etc.). They may also pave the way to novel technological applications (noise-- hanced reaction rates, noise-induced transport and separation on the na- scale, etc.). Key words to be mentioned in this context are stochastic r- onance, Brownian motors or ratchets, and noise-supported phenomena in excitable systems.

The Dynkin Festschrift

Mark I. Freidlin
The Dynkin Festschrift Book PDF

Author : Mark I. Freidlin
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 48,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461202790

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The Dynkin Festschrift by Mark I. Freidlin Pdf

Onishchik, A. A. Kirillov, and E. B. Vinberg, who obtained their first results on Lie groups in Dynkin's seminar. At a later stage, the work of the seminar was greatly enriched by the active participation of 1. 1. Pyatetskii Shapiro. As already noted, Dynkin started to work in probability as far back as his undergraduate studies. In fact, his first published paper deals with a problem arising in Markov chain theory. The most significant among his earliest probabilistic results concern sufficient statistics. In [15] and [17], Dynkin described all families of one-dimensional probability distributions admitting non-trivial sufficient statistics. These papers have considerably influenced the subsequent research in this field. But Dynkin's most famous results in probability concern the theory of Markov processes. Following Kolmogorov, Feller, Doob and Ito, Dynkin opened a new chapter in the theory of Markov processes. He created the fundamental concept of a Markov process as a family of measures corresponding to var ious initial times and states and he defined time homogeneous processes in terms of the shift operators ()t. In a joint paper with his student A.