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| 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 | : Malempati M. Rao |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 629 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 1475765983 |
Stochastic Processes: General Theory starts with the fundamental existence theorem of Kolmogorov, together with several of its extensions to stochastic processes. It treats the function theoretical aspects of processes and includes an extended account of martingales and their generalizations. Various compositions of (quasi- or semi-)martingales and their integrals are given. Here the Bochner boundedness principle plays a unifying role: a unique feature of the book. Applications to higher order stochastic differential equations and their special features are presented in detail. Stochastic processes in a manifold and multiparameter stochastic analysis are also discussed. Each of the seven chapters includes complements, exercises and extensive references: many avenues of research are suggested. The book is a completely revised and enlarged version of the author's Stochastic Processes and Integration (Noordhoff, 1979). The new title reflects the content and generality of the extensive amount of new material. Audience: Suitable as a text/reference for second year graduate classes and seminars. A knowledge of real analysis, including Lebesgue integration, is a prerequisite.
| Author | : Zeev Schuss |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 486 |
| Release | : 2009-12-09 |
| Genre | : Mathematics |
| ISBN | : 1441916059 |
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 | : D.R. Cox |
| Publisher | : Routledge |
| Total Pages | : 408 |
| Release | : 2017-09-04 |
| Genre | : Mathematics |
| ISBN | : 135140895X |
This book should be of interest to undergraduate and postgraduate students of probability theory.
| Author | : Pierre Brémaud |
| Publisher | : Springer Nature |
| Total Pages | : 713 |
| Release | : 2020-04-07 |
| Genre | : Mathematics |
| ISBN | : 3030401839 |
The ultimate objective of this book is to present a panoramic view of the main stochastic processes which have an impact on applications, with complete proofs and exercises. Random processes play a central role in the applied sciences, including operations research, insurance, finance, biology, physics, computer and communications networks, and signal processing. In order to help the reader to reach a level of technical autonomy sufficient to understand the presented models, this book includes a reasonable dose of probability theory. On the other hand, the study of stochastic processes gives an opportunity to apply the main theoretical results of probability theory beyond classroom examples and in a non-trivial manner that makes this discipline look more attractive to the applications-oriented student. One can distinguish three parts of this book. The first four chapters are about probability theory, Chapters 5 to 8 concern random sequences, or discrete-time stochastic processes, and the rest of the book focuses on stochastic processes and point processes. There is sufficient modularity for the instructor or the self-teaching reader to design a course or a study program adapted to her/his specific needs. This book is in a large measure self-contained.
| Author | : Jeffrey S Rosenthal |
| Publisher | : World Scientific |
| Total Pages | : 213 |
| Release | : 2019-09-26 |
| Genre | : Mathematics |
| ISBN | : 9811207925 |
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 | : Pierre Del Moral |
| Publisher | : CRC Press |
| Total Pages | : 866 |
| Release | : 2017-02-24 |
| Genre | : Mathematics |
| ISBN | : 1498701841 |
Unlike traditional books presenting stochastic processes in an academic way, this book includes concrete applications that students will find interesting such as gambling, finance, physics, signal processing, statistics, fractals, and biology. Written with an important illustrated guide in the beginning, it contains many illustrations, photos and pictures, along with several website links. Computational tools such as simulation and Monte Carlo methods are included as well as complete toolboxes for both traditional and new computational techniques.
| Author | : Anatolij V. Skorochod |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 192 |
| Release | : 2019-01-14 |
| Genre | : Mathematics |
| ISBN | : 3110618168 |
No detailed description available for "Lectures on the Theory of Stochastic Processes".
| Author | : Jean Jacod |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 620 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 3662025140 |
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.
| 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.
