Stochastic Processes and Applications PDF Download

Author: Grigorios A. Pavliotis
Publisher: Springer
ISBN: 1493913239
Category : Mathematics
Languages : en
Pages : 345

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Book Description
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: Marius Iosifescu
Publisher: Courier Corporation
ISBN: 0486150585
Category : Mathematics
Languages : en
Pages : 305

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Book Description
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.

Author: Oliver Ibe
Publisher: Newnes
ISBN: 0124078397
Category : Mathematics
Languages : en
Pages : 515

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Book Description
Markov processes are processes that have limited memory. In particular, their dependence on the past is only through the previous state. They are used to model the behavior of many systems including communications systems, transportation networks, image segmentation and analysis, biological systems and DNA sequence analysis, random atomic motion and diffusion in physics, social mobility, population studies, epidemiology, animal and insect migration, queueing systems, resource management, dams, financial engineering, actuarial science, and decision systems. Covering a wide range of areas of application of Markov processes, this second edition is revised to highlight the most important aspects as well as the most recent trends and applications of Markov processes. The author spent over 16 years in the industry before returning to academia, and he has applied many of the principles covered in this book in multiple research projects. Therefore, this is an applications-oriented book that also includes enough theory to provide a solid ground in the subject for the reader. - Presents both the theory and applications of the different aspects of Markov processes - Includes numerous solved examples as well as detailed diagrams that make it easier to understand the principle being presented - Discusses different applications of hidden Markov models, such as DNA sequence analysis and speech analysis.

Author: Petar Todorovic
Publisher: Springer Science & Business Media
ISBN: 1461397421
Category : Mathematics
Languages : en
Pages : 302

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Book Description
This text on stochastic processes and their applications is based on a set of lectures given during the past several years at the University of California, Santa Barbara (UCSB). It is an introductory graduate course designed for classroom purposes. Its objective is to provide graduate students of statistics with an overview of some basic methods and techniques in the theory of stochastic processes. The only prerequisites are some rudiments of measure and integration theory and an intermediate course in probability theory. There are more than 50 examples and applications and 243 problems and complements which appear at the end of each chapter. The book consists of 10 chapters. Basic concepts and definitions are pro vided in Chapter 1. This chapter also contains a number of motivating ex amples and applications illustrating the practical use of the concepts. The last five sections are devoted to topics such as separability, continuity, and measurability of random processes, which are discussed in some detail. The concept of a simple point process on R+ is introduced in Chapter 2. Using the coupling inequality and Le Cam's lemma, it is shown that if its counting function is stochastically continuous and has independent increments, the point process is Poisson. When the counting function is Markovian, the sequence of arrival times is also a Markov process. Some related topics such as independent thinning and marked point processes are also discussed. In the final section, an application of these results to flood modeling is presented.

Author: Richard Serfozo
Publisher: Springer Science & Business Media
ISBN: 3540893326
Category : Mathematics
Languages : en
Pages : 452

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Book Description
Stochastic processes are mathematical models of random phenomena that evolve according to prescribed dynamics. Processes commonly used in applications are Markov chains in discrete and continuous time, renewal and regenerative processes, Poisson processes, and Brownian motion. This volume gives an in-depth description of the structure and basic properties of these stochastic processes. A main focus is on equilibrium distributions, strong laws of large numbers, and ordinary and functional central limit theorems for cost and performance parameters. Although these results differ for various processes, they have a common trait of being limit theorems for processes with regenerative increments. Extensive examples and exercises show how to formulate stochastic models of systems as functions of a system’s data and dynamics, and how to represent and analyze cost and performance measures. Topics include stochastic networks, spatial and space-time Poisson processes, queueing, reversible processes, simulation, Brownian approximations, and varied Markovian models. The technical level of the volume is between that of introductory texts that focus on highlights of applied stochastic processes, and advanced texts that focus on theoretical aspects of processes.

Author: Rabi N. Bhattacharya
Publisher: SIAM
ISBN: 0898716896
Category : Mathematics
Languages : en
Pages : 726

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Book Description
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.

Author: M.J. Beckmann
Publisher: Springer Science & Business Media
ISBN: 364258201X
Category : Mathematics
Languages : en
Pages : 334

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Book Description
A volume of this nature containing a collection of papers has been brought out to honour a gentleman - a friend and a colleague - whose work has, to a large extent, advanced and popularized the use of stochastic point processes. Professor Srinivasan celebrated his sixt~ first 1:!irth d~ on December 16,1990 and will be retiring as Professor of Applied Mathematics from the Indian Institute of Technolo~, Madras on June 30,1991. In view of his outstanding contributions to the theor~ and applications of stochastic processes over a time span of thirt~ ~ears, it seemed appropriate not to let his birth d~ and retirement pass unnoticed. A s~posium in his honour and the publication of the proceedings appeared to us to be the most natural and sui table ~ to mark the occasion. The Indian Societ~ for ProbabU it~ and Statistics volunteered to organize the S~posium as part of their XII Annual conference in Bomba~. We requested a number of long-time friends, colleagues and former students of Professor Srinivasan to contribute a paper preferabl~ in the area of stochastic processes and their applications. The positive response and the enthusiastic cooperation of these distinguished scientists have resulted in the present collection. The contributions to this volume are divided into four parts: Stochastic Theor~ (2 articles), P~sics (6 articles), Biolo~ (4 articles) and Operations Research (12 articles). In addition the ke~note address delivered b~ Professor Srinivasan in the S~posium is also included.

Author: Norman T. J. Bailey
Publisher: John Wiley & Sons
ISBN: 9780471523680
Category : Mathematics
Languages : en
Pages : 268

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Book Description
Develops an introductory and relatively simple account of the theory and application of the evolutionary type of stochastic process. Professor Bailey adopts the heuristic approach of applied mathematics and develops both theoretical principles and applied techniques simultaneously.

Author: Richard Durrett
Publisher: Springer
ISBN: 3319456148
Category : Mathematics
Languages : en
Pages : 282

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Book Description
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.

Author: Serguei Primak
Publisher: John Wiley & Sons
ISBN: 0470021179
Category : Technology & Engineering
Languages : en
Pages : 446

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Book Description
Stochastic Methods & their Applications to Communications presents a valuable approach to the modelling, synthesis and numerical simulation of random processes with applications in communications and related fields. The authors provide a detailed account of random processes from an engineering point of view and illustrate the concepts with examples taken from the communications area. The discussions mainly focus on the analysis and synthesis of Markov models of random processes as applied to modelling such phenomena as interference and fading in communications. Encompassing both theory and practice, this original text provides a unified approach to the analysis and generation of continuous, impulsive and mixed random processes based on the Fokker-Planck equation for Markov processes. Presents the cumulated analysis of Markov processes Offers a SDE (Stochastic Differential Equations) approach to the generation of random processes with specified characteristics Includes the modelling of communication channels and interfer ences using SDE Features new results and techniques for the of solution of the generalized Fokker-Planck equation Essential reading for researchers, engineers, and graduate and upper year undergraduate students in the field of communications, signal processing, control, physics and other areas of science, this reference will have wide ranging appeal.