Studies in the Theory of Random Processes
Author | : Anatoliĭ Vladimirovich Skorokhod |
Publisher | : |
Total Pages | : 216 |
Release | : 1965 |
Genre | : Probabilities |
ISBN | : |
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Author | : Anatoliĭ Vladimirovich Skorokhod |
Publisher | : |
Total Pages | : 216 |
Release | : 1965 |
Genre | : Probabilities |
ISBN | : |
Author | : A. V. Skorokhod |
Publisher | : Courier Corporation |
Total Pages | : 209 |
Release | : 2014-07-28 |
Genre | : Mathematics |
ISBN | : 0486781461 |
Three-part treatment introduces basics plus theory of stochastic differential equations and various limit theorems connected with convergence of sequence of Markov chains to Markov process with continuous time. 1965 edition.
Author | : Iosif I. Gikhman |
Publisher | : Springer |
Total Pages | : 587 |
Release | : 2015-03-30 |
Genre | : Mathematics |
ISBN | : 3642619436 |
From the Reviews: "Gihman and Skorohod have done an excellent job of presenting the theory in its present state of rich imperfection." --D.W. Stroock, Bulletin of the American Mathematical Society, 1980
Author | : Anatolij Vladimiroviď Skorochod |
Publisher | : |
Total Pages | : 199 |
Release | : 1965 |
Genre | : |
ISBN | : |
Author | : Igor N. Kovalenko |
Publisher | : CRC Press |
Total Pages | : 456 |
Release | : 1996-07-08 |
Genre | : Mathematics |
ISBN | : 9780849328701 |
Devising and investigating random processes that describe mathematical models of phenomena is a major aspect of probability theory applications. Stochastic methods have penetrated into an unimaginably wide scope of problems encountered by researchers who need stochastic methods to solve problems and further their studies. This handbook supplies the knowledge you need on the modern theory of random processes. Packed with methods, Models of Random Processes: A Handbook for Mathematicians and Engineers presents definitions and properties on such widespread processes as Poisson, Markov, semi-Markov, Gaussian, and branching processes, and on special processes such as cluster, self-exiting, double stochastic Poisson, Gauss-Poisson, and extremal processes occurring in a variety of different practical problems. The handbook is based on an axiomatic definition of probability space, with strict definitions and constructions of random processes. Emphasis is placed on the constructive definition of each class of random processes, so that a process is explicitly defined by a sequence of independent random variables and can easily be implemented into the modelling. Models of Random Processes: A Handbook for Mathematicians and Engineers will be useful to researchers, engineers, postgraduate students and teachers in the fields of mathematics, physics, engineering, operations research, system analysis, econometrics, and many others.
Author | : Iosif Il?ich Gikhman |
Publisher | : Courier Corporation |
Total Pages | : 537 |
Release | : 1996-01-01 |
Genre | : Mathematics |
ISBN | : 0486693872 |
Rigorous exposition suitable for elementary instruction. Covers measure theory, axiomatization of probability theory, processes with independent increments, Markov processes and limit theorems for random processes, more. A wealth of results, ideas, and techniques distinguish this text. Introduction. Bibliography. 1969 edition.
Author | : Nikolaĭ Vladimirovich Krylov |
Publisher | : American Mathematical Soc. |
Total Pages | : 245 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 0821829858 |
This book concentrates on some general facts and ideas of the theory of stochastic processes. The topics include the Wiener process, stationary processes, infinitely divisible processes, and Ito stochastic equations. Basics of discrete time martingales are also presented and then used in one way or another throughout the book. Another common feature of the main body of the book is using stochastic integration with respect to random orthogonal measures. In particular, it is used forspectral representation of trajectories of stationary processes and for proving that Gaussian stationary processes with rational spectral densities are components of solutions to stochastic equations. In the case of infinitely divisible processes, stochastic integration allows for obtaining arepresentation of trajectories through jump measures. The Ito stochastic integral is also introduced as a particular case of stochastic integrals with respect to random orthogonal measures. Although it is not possible to cover even a noticeable portion of the topics listed above in a short book, it is hoped that after having followed the material presented here, the reader will have acquired a good understanding of what kind of results are available and what kind of techniques are used toobtain them. With more than 100 problems included, the book can serve as a text for an introductory course on stochastic processes or for independent study. Other works by this author published by the AMS include, Lectures on Elliptic and Parabolic Equations in Holder Spaces and Introduction to the Theoryof Diffusion Processes.
Author | : Leonid Koralov |
Publisher | : Springer Science & Business Media |
Total Pages | : 346 |
Release | : 2007-08-28 |
Genre | : Mathematics |
ISBN | : 3540254846 |
A one-year course in probability theory and the theory of random processes, taught at Princeton University to undergraduate and graduate students, forms the core of this book. It provides a comprehensive and self-contained exposition of classical probability theory and the theory of random processes. The book includes detailed discussion of Lebesgue integration, Markov chains, random walks, laws of large numbers, limit theorems, and their relation to Renormalization Group theory. It also includes the theory of stationary random processes, martingales, generalized random processes, and Brownian motion.