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Markov Processes And Related Problems Of Analysis

Author: Evgeniĭ Borisovich Dynkin
Publisher: Cambridge University Press
ISBN: 0521285127
Size: 59.84 MB
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The theory of Markov Processes has become a powerful tool in partial differential equations and potential theory with important applications to physics. Professor Dynkin has made many profound contributions to the subject and in this volume are collected several of his most important expository and survey articles. The content of these articles has not been covered in any monograph as yet. This account is accessible to graduate students in mathematics and operations research and will be welcomed by all those interested in stochastic processes and their applications.

Selected Papers Of E B Dynkin With Commentary

Author: Evgeniĭ Borisovich Dynkin
Publisher: American Mathematical Soc.
ISBN: 9780821810651
Size: 13.18 MB
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Eugene Dynkin is a rare example of a contemporary mathematician who has achieved outstanding results in two quite different areas of research: algebra and probability. In both areas, his ideas constitute an essential part of modern mathematical knowledge and form a basis for further development. Although his last work in algebra was published in 1955, his contributions continue to influence current research in algebra and in the physics of elementary particles. His work in probability is part of both the historical and the modern development of the topic. This volume presents Dynkin's scientific contributions in both areas. Included are Commentary by recognized experts in the corresponding fields who describe the time, place, role, and impact of Dynkin's research and achievements. Biographical notes and the recollections of his students are also featured.

Diffusion Processes And Related Problems In Analysis Volume Ii

Author: V. Wihstutz
Publisher: Springer Science & Business Media
ISBN: 1461203899
Size: 71.84 MB
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During the weekend of March 16-18, 1990 the University of North Carolina at Charlotte hosted a conference on the subject of stochastic flows, as part of a Special Activity Month in the Department of Mathematics. This conference was supported jointly by a National Science Foundation grant and by the University of North Carolina at Charlotte. Originally conceived as a regional conference for researchers in the Southeastern United States, the conference eventually drew participation from both coasts of the U. S. and from abroad. This broad-based par ticipation reflects a growing interest in the viewpoint of stochastic flows, particularly in probability theory and more generally in mathematics as a whole. While the theory of deterministic flows can be considered classical, the stochastic counterpart has only been developed in the past decade, through the efforts of Harris, Kunita, Elworthy, Baxendale and others. Much of this work was done in close connection with the theory of diffusion processes, where dynamical systems implicitly enter probability theory by means of stochastic differential equations. In this regard, the Charlotte conference served as a natural outgrowth of the Conference on Diffusion Processes, held at Northwestern University, Evanston Illinois in October 1989, the proceedings of which has now been published as Volume I of the current series. Due to this natural flow of ideas, and with the assistance and support of the Editorial Board, it was decided to organize the present two-volume effort.

Diffusion Processes And Related Problems In Analysis Stochastic Flows

Author: Mark A. Pinsky
Publisher: Birkhauser
ISBN: 9780817635435
Size: 43.17 MB
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A technical, but not specialized, presentation of stochastic flows for the general scientific community, in 15 reviewed papers from an international conference in Charlotte, North Carolina, March 1990. The broad topics cover general stochastic flows on manifolds, special flows and multipoint motions, infinite dimensional systems, invariant measures in real and white-noise-driven systems, and iterated function systems. No index. Annotation copyrighted by Book News, Inc., Portland, OR

Stochastic Processes And Functional Analysis

Author: Jerome Goldstein
Publisher: CRC Press
ISBN: 9780824798017
Size: 18.82 MB
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"Covers the areas of modern analysis and probability theory. Presents a collection of papers given at the Festschrift held in honor of the 65 birthday of M. M. Rao, whose prolific published research includes the well-received Marcel Dekker, Inc. books Theory of Orlicz Spaces and Conditional Measures and Applications. Features previously unpublished research articles by a host of internationally recognized scholars."

Stochastic Processes And Functional Analysis

Author: Alan C. Krinik
Publisher: CRC Press
ISBN: 9780203913574
Size: 12.62 MB
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This extraordinary compilation is an expansion of the recent American Mathematical Society Special Session celebrating M. M. Rao's distinguished career and includes most of the presented papers as well as ancillary contributions from session invitees. This book shows the effectiveness of abstract analysis for solving fundamental problems of stochastic theory, specifically the use of functional analytic methods for elucidating stochastic processes, as made manifest in M. M. Rao's prolific research achievements. Featuring a biography of M. M. Rao, a complete bibliography of his published works, and meditations from former students, the book includes contributions from over 30 notable researchers.

Markov Processes

Author: Evgenij Borisovic Dynkin
Publisher: Springer Science & Business Media
ISBN: 3662000318
Size: 33.22 MB
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The modem theory of Markov processes has its origins in the studies of A. A. MARKOV (1906-1907) on sequences of experiments "connected in a chain" and in the attempts to describe mathematically the physical phenomenon known as Brownian motion (L. BACHELlER 1900, A. EIN STEIN 1905). The first correct mathematical construction of a Markov process with continuous trajectories was given by N. WIENER in 1923. (This process is often called the Wiener process.) The general theory of Markov processes was developed in the 1930's and 1940's by A. N. KOL MOGOROV, W. FELLER, W. DOEBLlN, P. LEVY, J. L. DOOB, and others. During the past ten years the theory of Markov processes has entered a new period of intensive development. The methods of the theory of semigroups of linear operators made possible further progress in the classification of Markov processes by their infinitesimal characteristics. The broad classes of Markov processes with continuous trajectories be came the main object of study. The connections between Markov pro cesses and classical analysis were further developed. It has become possible not only to apply the results and methods of analysis to the problems of probability theory, but also to investigate analytic problems using probabilistic methods. Remarkable new connections between Markov processes and potential theory were revealed. The foundations of the theory were reviewed critically: the new concept of strong Markov process acquired for the whole theory of Markov processes great importance.

Markov Processes For Stochastic Modeling

Author: Masaaki Kijima
Publisher: CRC Press
ISBN: 9780412606601
Size: 54.30 MB
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This book presents an algebraic development of the theory of countable state space Markov chains with discrete and continuous time parameters.

Stochastic Analysis And Related Topics

Author: Laurent Decreusefond
Publisher: Springer Science & Business Media
ISBN: 3642299822
Size: 26.68 MB
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Since the early eighties, Ali Süleyman Üstünel has been one of the main contributors to the field of Malliavin calculus. In a workshop held in Paris, June 2010 several prominent researchers gave exciting talks in honor of his 60th birthday. The present volume includes scientific contributions from this workshop. Probability theory is first and foremost aimed at solving real-life problems containing randomness. Markov processes are one of the key tools for modeling that plays a vital part concerning such problems. Contributions on inventory control, mutation-selection in genetics and public-private partnerships illustrate several applications in this volume. Stochastic differential equations, be they partial or ordinary, also play a key role in stochastic modeling. Two of the contributions analyze examples that share a focus on probabilistic tools, namely stochastic analysis and stochastic calculus. Three other papers are devoted more to the theoretical development of these aspects. The volume addresses graduate students and researchers interested in stochastic analysis and its applications.