Stochastic Process Limits
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Stochastic Process Limits
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Author : Ward Whitt
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-11
Stochastic Process Limits written by Ward Whitt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-11 with Mathematics categories.
Stochastic Process Limits are useful and interesting because they generate simple approximations for complicated stochastic processes and also help explain the statistical regularity associated with a macroscopic view of uncertainty. This book emphasizes the continuous-mapping approach to obtain new stochastic-process limits from previously established stochastic-process limits. The continuous-mapping approach is applied to obtain heavy-traffic-stochastic-process limits for queueing models, including the case in which there are unmatched jumps in the limit process. These heavy-traffic limits generate simple approximations for complicated queueing processes and they reveal the impact of variability upon queueing performance. The book will be of interest to researchers and graduate students working in the areas of probability, stochastic processes, and operations research. In addition this book won the 2003 Lanchester Prize for the best contribution to Operation Research and Management in English, see: http://www.informs.org/Prizes/LanchesterPrize.html
Limit Theorems For Stochastic Processes
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Author : Jean Jacod
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Limit Theorems For Stochastic Processes written by Jean Jacod and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Initially the theory of convergence in law of stochastic processes was developed quite independently from the theory of martingales, semimartingales and stochastic integrals. Apart from a few exceptions essentially concerning diffusion processes, it is only recently that the relation between the two theories has been thoroughly studied. The authors of this Grundlehren volume, two of the international leaders in the field, propose a systematic exposition of convergence in law for stochastic processes, from the point of view of semimartingale theory, with emphasis on results that are useful for mathematical theory and mathematical statistics. This leads them to develop in detail some particularly useful parts of the general theory of stochastic processes, such as martingale problems, and absolute continuity or contiguity results. The book contains an elementary introduction to the main topics: theory of martingales and stochastic integrales, Skorokhod topology, etc., as well as a large number of results which have never appeared in book form, and some entirely new results. It should be useful to the professional probabilist or mathematical statistician, and of interest also to graduate students.
Stochastic Networks And Queues
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Author : Philippe Robert
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Stochastic Networks And Queues written by Philippe Robert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
Queues and stochastic networks are analyzed in this book with purely probabilistic methods. The purpose of these lectures is to show that general results from Markov processes, martingales or ergodic theory can be used directly to study the corresponding stochastic processes. Recent developments have shown that, instead of having ad-hoc methods, a better understanding of fundamental results on stochastic processes is crucial to study the complex behavior of stochastic networks. In this book, various aspects of these stochastic models are investigated in depth in an elementary way: Existence of equilibrium, characterization of stationary regimes, transient behaviors (rare events, hitting times) and critical regimes, etc. A simple presentation of stationary point processes and Palm measures is given. Scaling methods and functional limit theorems are a major theme of this book. In particular, a complete chapter is devoted to fluid limits of Markov processes.
Stochastic Processes And Applications
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Author : Grigorios A. Pavliotis
language : en
Publisher: Springer
Release Date : 2014-11-19
Stochastic Processes And Applications written by Grigorios A. Pavliotis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-19 with Mathematics categories.
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.
Basic Stochastic Processes
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Author : Zdzislaw Brzezniak
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Basic Stochastic Processes written by Zdzislaw Brzezniak and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Stochastic processes are tools used widely by statisticians and researchers working in the mathematics of finance. This book for self-study provides a detailed treatment of conditional expectation and probability, a topic that in principle belongs to probability theory, but is essential as a tool for stochastic processes. The book centers on exercises as the main means of explanation.
Measure Valued Branching Markov Processes
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Author : Zenghu Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-10
Measure Valued Branching Markov Processes written by Zenghu Li and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-10 with Mathematics categories.
Measure-valued branching processes arise as high density limits of branching particle systems. The Dawson-Watanabe superprocess is a special class of those. The author constructs superprocesses with Borel right underlying motions and general branching mechanisms and shows the existence of their Borel right realizations. He then uses transformations to derive the existence and regularity of several different forms of the superprocesses. This treatment simplifies the constructions and gives useful perspectives. Martingale problems of superprocesses are discussed under Feller type assumptions. The most important feature of the book is the systematic treatment of immigration superprocesses and generalized Ornstein--Uhlenbeck processes based on skew convolution semigroups. The volume addresses researchers in measure-valued processes, branching processes, stochastic analysis, biological and genetic models, and graduate students in probability theory and stochastic processes.
Random Processes For Engineers
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Author : Bruce Hajek
language : en
Publisher: Cambridge University Press
Release Date : 2015-03-12
Random Processes For Engineers written by Bruce Hajek and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-12 with Computers categories.
An engaging introduction to the critical tools needed to design and evaluate engineering systems operating in uncertain environments.
Convergence Of Stochastic Processes
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Author : D. Pollard
language : en
Publisher: David Pollard
Release Date : 1984-10-08
Convergence Of Stochastic Processes written by D. Pollard and has been published by David Pollard this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-10-08 with Mathematics categories.
Functionals on stochastic processes; Uniform convergence of empirical measures; Convergence in distribution in euclidean spaces; Convergence in distribution in metric spaces; The uniform metric on space of cadlag functions; The skorohod metric on D [0, oo); Central limit teorems; Martingales.
Stochastic Processes With Applications
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Author : Rabi N. Bhattacharya
language : en
Publisher: SIAM
Release Date : 2009-08-27
Stochastic Processes With Applications written by Rabi N. Bhattacharya and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-27 with Mathematics categories.
This book develops systematically and rigorously, yet in an expository and lively manner, the evolution of general random processes and their large time properties such as transience, recurrence, and convergence to steady states. The emphasis is on the most important classes of these processes from the viewpoint of theory as well as applications, namely, Markov processes. The book features very broad coverage of the most applicable aspects of stochastic processes, including sufficient material for self-contained courses on random walks in one and multiple dimensions; Markov chains in discrete and continuous times, including birth-death processes; Brownian motion and diffusions; stochastic optimization; and stochastic differential equations. This book is for graduate students in mathematics, statistics, science and engineering, and it may also be used as a reference by professionals in diverse fields whose work involves the application of probability.
Essentials Of Stochastic Processes
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Author : Richard Durrett
language : en
Publisher: Springer
Release Date : 2016-11-07
Essentials Of Stochastic Processes written by Richard Durrett and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-07 with Mathematics categories.
Building upon the previous editions, this textbook is a first course in stochastic processes taken by undergraduate and graduate students (MS and PhD students from math, statistics, economics, computer science, engineering, and finance departments) who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and option pricing. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding. Drawing from teaching experience and student feedback, there are many new examples and problems with solutions that use TI-83 to eliminate the tedious details of solving linear equations by hand, and the collection of exercises is much improved, with many more biological examples. Originally included in previous editions, material too advanced for this first course in stochastic processes has been eliminated while treatment of other topics useful for applications has been expanded. In addition, the ordering of topics has been improved; for example, the difficult subject of martingales is delayed until its usefulness can be applied in the treatment of mathematical finance.