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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 | : I. I. Gihman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 393 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 146158065X |
It was originally planned that the Theory of Stochastic Processes would consist of two volumes: the first to be devoted to general problems and the second to specific cJasses of random processes. It became apparent, however, that the amount of material related to specific problems of the theory could not possibly be incJuded in one volume. This is how the present third volume came into being. This voJume contains the theory of martingales, stochastic integrals, stochastic differential equations, diffusion, and continuous Markov processes. The theory of stochastic processes is an actively developing branch of mathe matics, and it would be an unreasonable and impossible task to attempt to encompass it in a single treatise (even a multivolume one). Therefore, the authors, guided by their own considerations concerning the relative importance of various results, naturally had to be selective in their choice of material. The authors are fully aware that such a selective process is not perfecL Even a number of topics that are, in the authors' opinion, of great importance could not be incJuded, for example, limit theorems for particular cJasses of random processes, the theory of random fields, conditional Markov processes, and information and statistics of random processes. With the publication of this last volume, we recall with gratitude oUf associates who assisted us in this endeavor, and express our sincere thanks to G.N. Sytaya, L.V. Lobanova, P.V. Boiko, N.F. Ryabova, N.A. Skorohod, V.V. Skorohod, N.I. Portenko, and L.I. Gab.
| Author | : Yurij V. Prokhorov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 260 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 3662036401 |
This volume of the Encyclopaedia is a survey of stochastic calculus, an increasingly important part of probability, authored by well-known experts in the field. The book addresses graduate students and researchers in probability theory and mathematical statistics, as well as physicists and engineers who need to apply stochastic methods.
| 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 | : Iosif I. Gikhman |
| Publisher | : |
| Total Pages | : 404 |
| Release | : 2007-03-20 |
| Genre | : Mathematics |
| ISBN | : |
This work presents the theory of stochastic processes in its present state of rich imperfection. To describe this work as encyclopedic does not give an accurate picture of its content and style. Some parts read like a textbook, but others are more technical and contain relatively new results. The exposition is robust and explicit, as one has come to expect of the Russian tradition of mathematical writing. The authors' display mastery of their material, and demonstrate their confident insight into its underlying structure. The set when completed will be an invaluable source of information and reference in this ever-expanding field.
| 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 | : 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 | : 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 | : I. I. Gihman |
| Publisher | : Springer |
| Total Pages | : 388 |
| Release | : 2012-11-25 |
| Genre | : Mathematics |
| ISBN | : 9781461580676 |
It was originally planned that the Theory of Stochastic Processes would consist of two volumes: the first to be devoted to general problems and the second to specific cJasses of random processes. It became apparent, however, that the amount of material related to specific problems of the theory could not possibly be incJuded in one volume. This is how the present third volume came into being. This voJume contains the theory of martingales, stochastic integrals, stochastic differential equations, diffusion, and continuous Markov processes. The theory of stochastic processes is an actively developing branch of mathe matics, and it would be an unreasonable and impossible task to attempt to encompass it in a single treatise (even a multivolume one). Therefore, the authors, guided by their own considerations concerning the relative importance of various results, naturally had to be selective in their choice of material. The authors are fully aware that such a selective process is not perfecL Even a number of topics that are, in the authors' opinion, of great importance could not be incJuded, for example, limit theorems for particular cJasses of random processes, the theory of random fields, conditional Markov processes, and information and statistics of random processes. With the publication of this last volume, we recall with gratitude oUf associates who assisted us in this endeavor, and express our sincere thanks to G. N. Sytaya, L. V. Lobanova, P. V. Boiko, N. F. Ryabova, N. A. Skorohod, V. V. Skorohod, N. I. Portenko, and L. I. Gab.
| 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".
