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• Author : N.G. Van Kampen
• Publisher :Unknown
• Release Date :1992-11-20
• Total pages :480
• ISBN : 9780080571386

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Summary : This new edition of Van Kampen's standard work has been completely revised and updated. Three major changes have also been made. The Langevin equation receives more attention in a separate chapter in which non-Gaussian and colored noise are introduced. Another additional chapter contains old and new material on first-passage times and related subjects which lay the foundation for the chapter on unstable systems. Finally a completely new chapter has been written on the quantum mechanical foundations of noise. The references have also been expanded and updated.

• Author : N.G. Van Kampen
• Publisher :Unknown
• Release Date :2011-08-30
• Total pages :464
• ISBN : 0080475361

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Summary : 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

• Author : N. G. van Kampen
• Publisher :Unknown
• Release Date :1981
• Total pages :419
• ISBN : UOM:39015053348259

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Summary : This new edition of Van Kampen's standard work has been completely revised and updated. Three major changes have also been made. The Langevin equation receives more attention in a separate chapter in which non-Gaussian and colored noise are introduced. Another additional chapter contains old and new material on first-passage times and related subjects which lay the foundation for the chapter on unstable systems. Finally a completely new chapter has been written on the quantum mechanical foundations of noise. The references have also been expanded and updated.

• Author : Jan A. Freund,Thorsten Pöschel
• Publisher :Unknown
• Release Date :2008-01-11
• Total pages :518
• ISBN : 9783540453963

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Summary : 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.

• Author : Kurt Jacobs
• Publisher :Unknown
• Release Date :2010-02-18
• Total pages :204
• ISBN : 9781139486798

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Summary : Stochastic processes are an essential part of numerous branches of physics, as well as in biology, chemistry, and finance. This textbook provides a solid understanding of stochastic processes and stochastic calculus in physics, without the need for measure theory. In avoiding measure theory, this textbook gives readers the tools necessary to use stochastic methods in research with a minimum of mathematical background. Coverage of the more exotic Levy processes is included, as is a concise account of numerical methods for simulating stochastic systems driven by Gaussian noise. The book concludes with a non-technical introduction to the concepts and jargon of measure-theoretic probability theory. With over 70 exercises, this textbook is an easily accessible introduction to stochastic processes and their applications, as well as methods for numerical simulation, for graduate students and researchers in physics.

• Author : K. E. Shuler
• Publisher :Unknown
• Release Date :2009-09-08
• Total pages :391
• ISBN : 9780470144008

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Summary : The Advances in Chemical Physics series provides the chemical physics and physical chemistry fields with a forum for critical, authoritative evaluations of advances in every area of the discipline. Filled with cutting-edge research reported in a cohesive manner not found elsewhere in the literature, each volume of the Advances in Chemical Physics series serves as the perfect supplement to any advanced graduate class devoted to the study of chemical physics.

• Author : Masao Nagasawa
• Publisher :Unknown
• Release Date :2012-12-06
• Total pages :598
• ISBN : 9783034883832

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Summary : From the reviews: "The text is almost self-contained and requires only an elementary knowledge of probability theory at the graduate level. The book under review is recommended to mathematicians, physicists and graduate students interested in mathematical physics and stochastic processes. Furthermore, some selected chapters can be used as sub-textbooks for advanced courses on stochastic processes, quantum theory and quantum chemistry." ZAA

• Author : William Coffey,Yu. P. Kalmykov,J. T. Waldron
• Publisher :Unknown
• Release Date :1996
• Total pages :413
• ISBN : 9810216513

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Summary : The book is suitable for a lecture course on the theory of Brownian motion, being based on final year undergraduate lectures given at Trinity College, Dublin. Topics that are discussed include: white noise; the Chapman-Kolmogorov equation ? Kramers-Moyal expansion; the Langevin equation; the Fokker-Planck equation; Brownian motion of a free particle; spectral density and the Wiener-Khintchin theorem ? Brownian motion in a potential application to the Josephson effect, ring laser gyro; Brownian motion in two dimensions; harmonic oscillators; itinerant oscillators; linear response theory; rotational Brownian motion; application to loss processes in dielectric and ferrofluids; superparamagnetism and nonlinear relaxation processes.As the first elementary book on the Langevin equation approach to Brownian motion, this volume attempts to fill in all the missing details which students find particularly hard to comprehend from the fundamental papers contained in the Dover reprint ? Selected Papers on Noise and Stochastic Processes, ed. N Wax (1954) ? together with modern applications particularly to relaxation in ferrofluids and polar dielectrics.

• Author : Raúl Toral,Pere Colet
• Publisher :Unknown
• Release Date :2014-06-26
• Total pages :416
• ISBN : 9783527683123

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Summary : Stochastic Numerical Methods introduces at Master level the numerical methods that use probability or stochastic concepts to analyze random processes. The book aims at being rather general and is addressed at students of natural sciences (Physics, Chemistry, Mathematics, Biology, etc.) and Engineering, but also social sciences (Economy, Sociology, etc.) where some of the techniques have been used recently to numerically simulate different agent-based models. Examples included in the book range from phase-transitions and critical phenomena, including details of data analysis (extraction of critical exponents, finite-size effects, etc.), to population dynamics, interfacial growth, chemical reactions, etc. Program listings are integrated in the discussion of numerical algorithms to facilitate their understanding. From the contents: Review of Probability Concepts Monte Carlo Integration Generation of Uniform and Non-uniform Random Numbers: Non-correlated Values Dynamical Methods Applications to Statistical Mechanics Introduction to Stochastic Processes Numerical Simulation of Ordinary and Partial Stochastic Differential Equations Introduction to Master Equations Numerical Simulations of Master Equations Hybrid Monte Carlo Generation of n-Dimensional Correlated Gaussian Variables Collective Algorithms for Spin Systems Histogram Extrapolation Multicanonical Simulations

• Author : Zeev Schuss
• Publisher :Unknown
• Release Date :2009-12-09
• Total pages :468
• ISBN : 9781441916051

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Summary : Stochastic processes and diffusion theory are the mathematical underpinnings of many scientific disciplines, including statistical physics, physical chemistry, molecular biophysics, communications theory and many more. Many books, reviews and research articles have been published on this topic, from the purely mathematical to the most practical. This book offers an analytical approach to stochastic processes that are most common in the physical and life sciences, as well as in optimal control and in the theory of filltering of signals from noisy measurements. Its aim is to make probability theory in function space readily accessible to scientists trained in the traditional methods of applied mathematics, such as integral, ordinary, and partial differential equations and asymptotic methods, rather than in probability and measure theory.

• Author : Kurt Egon Shuler
• Publisher :Unknown
• Release Date :1969
• Total pages :391
• ISBN : 0471789674

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Summary :

• Author : Horacio S Wio
• Publisher :Unknown
• Release Date :1994-02-07
• Total pages :232
• ISBN : 9789814502658

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Summary : The purpose of this textbook is to bring together, in a self-contained introductory form, the scattered material in the field of stochastic processes and statistical physics. It offers the opportunity of being acquainted with stochastic, kinetic and nonequilibrium processes. Although the research techniques in these areas have become standard procedures, they are not usually taught in the normal courses on statistical physics. For students of physics in their last year and graduate students who wish to gain an invaluable introduction on the above subjects, this book is a necessary tool. Contents:Stochastic Processes and the Master Equation:Stochastic ProcessesMarkovian ProcessesMaster EquationsKramers Moyal ExpansionBrownian Motion, Langevin and Fokker-Planck EquationsDistributions, BBGKY Hierarchy, Density Operator:Probability Density as a FluidBBGKY HierarchyMicroscopic Balance EquationsDensity OperatorLinear Nonequilibrium Thermodynamics and Onsager Relations:Onsager Regression to Equilibrium HypothesisOnsager RelationsMinimum Production of EntropyLinear Response Theory, Fluctuation-Dissipation Theorem:Correlation Functions: Definitions and PropertiesLinear Response TheoryFluctuation-Dissipation TheoremInstabilities and Far from Equilibrium Phase-Transitions:Limit Cycles, Bifurcations, Symmetry BreakingNoise Induced TransitionsFormation and Propagation of Patterns in Far from Equilibrium Systems:Reaction-Diffusion Descriptions and Pattern FormationPattern Propagation Readership: Graduate students in physics and chemistry. keywords:Stochastic Processes;Langevin and Fokker-Planck Equations;Statistical Physics;Onsager Relations;Linear Response;Nonequilibrium Statistical Physics;Transport Processes;Noise Induced Transitions;Instabilities;Pattern Formation and Propagation “This book introduces ways to investigate nonequilibrium statistical physics, mainly via stochastic processes, and presents results achieved with such methodology … it is suitable for seminars directed towards relatively mature students in theoretical physics or applied mathematics.” H Muthsam “The present book is a good choice for a single book covering the field … suitable for undergraduate students in the last year and graduate students. They will find in it a suggestive introduction that motivates them to dig deeper into the field and to look for those topics omitted from the text … highly recommended to anyone interested in becoming acquainted with nonequilibrium statistical physics.” Journal of Statistical Physics

• Author : Grigorios A. Pavliotis
• Publisher :Unknown
• Release Date :2014-11-19
• Total pages :339
• ISBN : 9781493913237

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Summary : This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.

• Author : L. Schimansky-Geier
• Publisher :Unknown
• Release Date :2007
• Total pages :452
• ISBN : 9789812706911

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Summary : Nonlinear dynamics of complex processes is an active research field with large numbers of publications in basic research, and broad applications from diverse fields of science. Nonlinear dynamics as manifested by deterministic and stochastic evolution models of complex behavior has entered statistical physics, physical chemistry, biophysics, geophysics, astrophysics, theoretical ecology, semiconductor physics and -optics, etc. This field of research has induced a new terminology in science connected with new questions, problems, solutions and methods. New scenarios have emerged for spatio-temporal structures in dynamical systems far from equilibrium. Their analysis and possible control are intriguing and challenging aspects of the current research. The duality of fundamental and applied research is a focal point of its main attractivity and fascination. Basic topics and foundations are always linked to concrete and precise examples. Models and measurements of complex nonlinear processes evoke and provoke new fundamental questions that diversify and broaden the mathematical concepts and tools. In return, new mathematical approaches to modeling and analysis enlarge the scope and efficiency of applied research.

• Author : Peter Schuster
• Publisher :Unknown
• Release Date :2016-10-14
• Total pages :718
• ISBN : 9783319395029

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Summary : This book has developed over the past fifteen years from a modern course on stochastic chemical kinetics for graduate students in physics, chemistry and biology. The first part presents a systematic collection of the mathematical background material needed to understand probability, statistics, and stochastic processes as a prerequisite for the increasingly challenging practical applications in chemistry and the life sciences examined in the second part. Recent advances in the development of new techniques and in the resolution of conventional experiments at nano-scales have been tremendous: today molecular spectroscopy can provide insights into processes down to scales at which current theories at the interface of physics, chemistry and the life sciences cannot be successful without a firm grasp of randomness and its sources. Routinely measured data is now sufficiently accurate to allow the direct recording of fluctuations. As a result, the sampling of data and the modeling of relevant processes are doomed to produce artifacts in interpretation unless the observer has a solid background in the mathematics of limited reproducibility. The material covered is presented in a modular approach, allowing more advanced sections to be skipped if the reader is primarily interested in applications. At the same time, most derivations of analytical solutions for the selected examples are provided in full length to guide more advanced readers in their attempts to derive solutions on their own. The book employs uniform notation throughout, and a glossary has been added to define the most important notions discussed.

• Author : Hans C. Öttinger
• Publisher :Unknown
• Release Date :2012-12-06
• Total pages :362
• ISBN : 9783642582905

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Summary : This book consists of two strongly interweaved parts: the mathematical theory of stochastic processes and its applications to molecular theories of polymeric fluids. The comprehensive mathematical background provided in the first section will be equally useful in many other branches of engineering and the natural sciences. The second part provides readers with a more direct understanding of polymer dynamics, allowing them to identify exactly solvable models more easily, and to develop efficient computer simulation algorithms in a straightforward manner. In view of the examples and applications to problems taken from the front line of science, this volume may be used both as a basic textbook or as a reference book. Program examples written in FORTRAN are available via ftp from ftp.springer.de/pub/chemistry/polysim/.

• Author : Liliana Blanco Castañeda,Viswanathan Arunachalam,Selvamuthu Dharmaraja
• Publisher :Unknown
• Release Date :2014-08-21
• Total pages :614
• ISBN : 9781118344965

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Summary : An easily accessible, real-world approach to probability andstochastic processes Introduction to Probability and Stochastic Processes withApplications presents a clear, easy-to-understand treatment ofprobability and stochastic processes, providing readers with asolid foundation they can build upon throughout their careers. Withan emphasis on applications in engineering, applied sciences,business and finance, statistics, mathematics, and operationsresearch, the book features numerous real-world examples thatillustrate how random phenomena occur in nature and how to useprobabilistic techniques to accurately model these phenomena. The authors discuss a broad range of topics, from the basicconcepts of probability to advanced topics for further study,including Itô integrals, martingales, and sigma algebras.Additional topical coverage includes: Distributions of discrete and continuous random variablesfrequently used in applications Random vectors, conditional probability, expectation, andmultivariate normal distributions The laws of large numbers, limit theorems, and convergence ofsequences of random variables Stochastic processes and related applications, particularly inqueueing systems Financial mathematics, including pricing methods such asrisk-neutral valuation and the Black-Scholes formula Extensive appendices containing a review of the requisitemathematics and tables of standard distributions for use inapplications are provided, and plentiful exercises, problems, andsolutions are found throughout. Also, a related website featuresadditional exercises with solutions and supplementary material forclassroom use. Introduction to Probability and StochasticProcesses with Applications is an ideal book for probabilitycourses at the upper-undergraduate level. The book is also avaluable reference for researchers and practitioners in the fieldsof engineering, operations research, and computer science whoconduct data analysis to make decisions in their everyday work.

• Author : Abraham Nitzan
• Publisher :Unknown
• Release Date :2006-04-06
• Total pages :719
• ISBN : 9780198529798

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Summary : Graduate level textbook presenting some of the most fundamental processes that underlie physical, chemical and biological phenomena in complex condensed phase systems. Includes in-depth descriptions of relevant methodologies, and provides ample introductory material for readers of different backgrounds.

• Author : Nelson Wax
• Publisher :Unknown
• Release Date :2014-08-20
• Total pages :352
• ISBN : 9780486798264

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Summary : Six classic papers, selected to meet the needs of physicists, applied mathematicians, and engineers, include contributions by S. Chandrasekhar, G. E. Uhlenbeck, L. S. Ornstein, Ming Chen Wang, others. 1954 edition.

• Author : Daniel T. Gillespie,S. GILLESPIE
• Publisher :Unknown
• Release Date :1992
• Total pages :565
• ISBN : 0122839552

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Summary : 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.

• Author : Ionut Florescu
• Publisher :Unknown
• Release Date :2014-10-27
• Total pages :576
• ISBN : 9780470624555

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Summary : A comprehensive and accessible presentation of probability and stochastic processes with emphasis on key theoretical concepts and real-world applications With a sophisticated approach, "Probability and Stochastic Processes" successfully balances theory and applications in a pedagogical and accessible format. The book's primary focus is on key theoretical notions in probability to provide a foundation for understanding concepts and examples related to stochastic processes. Organized into two main sections, the book begins by developing probability theory with topical coverage on probability measure; random variables; integration theory; product spaces, conditional distribution, and conditional expectations; and limit theorems. The second part explores stochastic processes and related concepts including the Poisson process, renewal processes, Markov chains, semi-Markov processes, martingales, and Brownian motion. Featuring a logical combination of traditional and complex theories as well as practices, "Probability and Stochastic Processes" also includes: Multiple examples from disciplines such as business, mathematical finance, and engineering Chapter-by-chapter exercises and examples to allow readers to test their comprehension of the presented material A rigorous treatment of all probability and stochastic processes concepts An appropriate textbook for probability and stochastic processes courses at the upper-undergraduate and graduate level in mathematics, business, and electrical engineering, "Probability and Stochastic Processes" is also an ideal reference for researchers and practitioners in the fields of mathematics, engineering, and finance. Ionut Florescu, PhD, is Research Associate Professor of Financial Engineering and Director of the Hanlon Financial Systems Lab at Stevens Institute of Technology. His areas of research interest include stochastic volatility, stochastic partial differential equations, Monte Carlo methods, and numerical methods for stochastic processes. He is also the coauthor of "Handbook of Probability" and coeditor of "Handbook of Modeling High-Frequency Data in Finance," both published by Wiley.