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Author: Robert B. Ash Publisher: Academic Press ISBN: 1483191435 Category : Mathematics Languages : en Pages : 332
Book Description
Topics in Stochastic Processes covers specific processes that have a definite physical interpretation and that explicit numerical results can be obtained. This book contains five chapters and begins with the L2 stochastic processes and the concept of prediction theory. The next chapter discusses the principles of ergodic theorem to real analysis, Markov chains, and information theory. Another chapter deals with the sample function behavior of continuous parameter processes. This chapter also explores the general properties of Martingales and Markov processes, as well as the one-dimensional Brownian motion. The aim of this chapter is to illustrate those concepts and constructions that are basic in any discussion of continuous parameter processes, and to provide insights to more advanced material on Markov processes and potential theory. The final chapter demonstrates the use of theory of continuous parameter processes to develop the Itô stochastic integral. This chapter also provides the solution of stochastic differential equations. This book will be of great value to mathematicians, engineers, and physicists.
Author: Robert B. Ash Publisher: Academic Press ISBN: 1483191435 Category : Mathematics Languages : en Pages : 332
Book Description
Topics in Stochastic Processes covers specific processes that have a definite physical interpretation and that explicit numerical results can be obtained. This book contains five chapters and begins with the L2 stochastic processes and the concept of prediction theory. The next chapter discusses the principles of ergodic theorem to real analysis, Markov chains, and information theory. Another chapter deals with the sample function behavior of continuous parameter processes. This chapter also explores the general properties of Martingales and Markov processes, as well as the one-dimensional Brownian motion. The aim of this chapter is to illustrate those concepts and constructions that are basic in any discussion of continuous parameter processes, and to provide insights to more advanced material on Markov processes and potential theory. The final chapter demonstrates the use of theory of continuous parameter processes to develop the Itô stochastic integral. This chapter also provides the solution of stochastic differential equations. This book will be of great value to mathematicians, engineers, and physicists.
Author: Robert B. Ash Publisher: ISBN: Category : Mathematics Languages : en Pages : 338
Book Description
Stochastic Processes, Introduction, Covariance functions, Second order calculus, Karhunen-loeve expansion, Estimation problems, Notes; Spectral theory and prediction, Introduction, L Stochastic integrals, Decomposition of stationary processes, Examples of discrete parameter processes, Discrete parameter prediction: Special cases, Discrete parameter prediction: General solution, Examples of continuous parameter processes; Continuos parameter prediction special cases; yaglom's method, Some stochastic differential equations, Continuos parameter prediction: remarks on the general solution, Notes; Ergodic theory, Ergodicity and mixing, The pointwise ergodic theorem, Applications to real analysis, Applications to Markov chains, The Shannon-mcMillan theorem, Notes; Sample function analysis of continuous parameter stochastic processes, Separability, Measurability, One-Dimensional brownian motion, Law of the iterated logarithm, Markov processes, Processes with independent increments, Continuous parameter martingales, The strong Markov property, Notes; The ito integral and stochastic differential equations, Definitions of the ito integral, Existence and uniqueness theorems for stochastic differential equations, Stochastic differentials: A chain rule, Notes.
Author: Jeff Englebert Publisher: CRC Press ISBN: 9782884490696 Category : Mathematics Languages : en Pages : 186
Book Description
The aim of this volume is to make accessible to a greater audience papers given at the 10th Winterschool on Stochastic Processes in Siegmundsburg, Germany, March 1994. The papers include developments in stochastic analysis, applications to finance mathematics, Markov processes and diffusion processes, stochastic differential equations and stochastic partial differential equations.
Author: Richard Durrett Publisher: Springer ISBN: 3319456148 Category : Mathematics Languages : en Pages : 282
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: Kurt Jacobs Publisher: Cambridge University Press ISBN: 1139486799 Category : Science Languages : en Pages : 203
Book Description
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: Petar Todorovic Publisher: Springer Science & Business Media ISBN: 1461397421 Category : Mathematics Languages : en Pages : 302
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: Jeffrey S Rosenthal Publisher: World Scientific ISBN: 9811207925 Category : Mathematics Languages : en Pages : 213
Book Description
This textbook introduces the theory of stochastic processes, that is, randomness which proceeds in time. Using concrete examples like repeated gambling and jumping frogs, it presents fundamental mathematical results through simple, clear, logical theorems and examples. It covers in detail such essential material as Markov chain recurrence criteria, the Markov chain convergence theorem, and optional stopping theorems for martingales. The final chapter provides a brief introduction to Brownian motion, Markov processes in continuous time and space, Poisson processes, and renewal theory.Interspersed throughout are applications to such topics as gambler's ruin probabilities, random walks on graphs, sequence waiting times, branching processes, stock option pricing, and Markov Chain Monte Carlo (MCMC) algorithms.The focus is always on making the theory as well-motivated and accessible as possible, to allow students and readers to learn this fascinating subject as easily and painlessly as possible.
Author: Dmytro Gusak Publisher: Springer Science & Business Media ISBN: 0387878629 Category : Mathematics Languages : en Pages : 379
Book Description
Providing the necessary materials within a theoretical framework, this volume presents stochastic principles and processes, and related areas. Over 1000 exercises illustrate the concepts discussed, including modern approaches to sample paths and optimal stopping.
Author: Rainer Buckdahn Publisher: CRC Press ISBN: 1482265230 Category : Mathematics Languages : en Pages : 296
Book Description
This volume comprises selected papers presented at the 12th Winter School on Stochastic Processes and their Applications, which was held in Siegmundsburg, Germany, in March 2000. The contents include Backward Stochastic Differential Equations; Semilinear PDE and SPDE; Arbitrage Theory; Credit Derivatives and Models for Correlated Defaults; Three In
Author: Ludger Rüschendorf Publisher: Springer Nature ISBN: 3662647117 Category : Mathematics Languages : en Pages : 310
Book Description
The book provides an introduction to advanced topics in stochastic processes and related stochastic analysis, and combines them with a sound presentation of the fundamentals of financial mathematics. It is wide-ranging in content, while at the same time placing much emphasis on good readability, motivation, and explanation of the issues covered. Financial mathematical topics are first introduced in the context of discrete time processes and then transferred to continuous-time models. The basic construction of the stochastic integral and the associated martingale theory provide fundamental methods of the theory of stochastic processes for the construction of suitable stochastic models of financial mathematics, e.g. using stochastic differential equations. Central results of stochastic analysis such as the Itô formula, Girsanov's theorem and martingale representation theorems are of fundamental importance in financial mathematics, e.g. for the risk-neutral valuation formula (Black-Scholes formula) or the question of the hedgeability of options and the completeness of market models. Chapters on the valuation of options in complete and incomplete markets and on the determination of optimal hedging strategies conclude the range of topics. Advanced knowledge of probability theory is assumed, in particular of discrete-time processes (martingales, Markov chains) and continuous-time processes (Brownian motion, Lévy processes, processes with independent increments, Markov processes). The book is thus suitable for advanced students as a companion reading and for instructors as a basis for their own courses. This book is a translation of the original German 1st edition Stochastische Prozesse und Finanzmathematik by Ludger Rüschendorf, published by Springer-Verlag GmbH Germany, part of Springer Nature in 2020. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com) and in a subsequent editing, improved by the author. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.
Author: Robert B. Ash
Author: Robert B. Ash
Author: Robert B. Ash
Author: Jeff Englebert
Author: Richard Durrett
Author: Kurt Jacobs
Author: Petar Todorovic
Author: Jeffrey S Rosenthal
Author: Dmytro Gusak
Author: Rainer Buckdahn
Author: Ludger Rüschendorf