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Author : M. Fukushima
Publisher : Unknown
Page : 316 pages
File Size : 53,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662214350
Author : M. Fukushima
Publisher : Springer
Page : 316 pages
File Size : 40,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540391555
Author : Adam Bobrowski
Publisher : Cambridge University Press
Page : 416 pages
File Size : 48,8 Mb
Release : 2005-08-11
Category : Mathematics
ISBN : 0521831660
This text presents selected areas of functional analysis that can facilitate an understanding of ideas in probability and stochastic processes. Topics covered include basic Hilbert and Banach spaces, weak topologies and Banach algebras, and the theory ofsemigroups of bounded linear operators.
Author : Kazuaki Taira
Publisher : Unknown
Page : 502 pages
File Size : 49,5 Mb
Release : 2020
Category : Boundary value problems
ISBN : 303048789X
This 3rd edition provides an insight into the mathematical crossroads formed by functional analysis (the macroscopic approach), partial differential equations (the mesoscopic approach) and probability (the microscopic approach) via the mathematics needed for the hard parts of Markov processes. It brings these three fields of analysis together, providing a comprehensive study of Markov processes from a broad perspective. The material is carefully and effectively explained, resulting in a surprisingly readable account of the subject. The main focus is on a powerful method for future research in elliptic boundary value problems and Markov processes via semigroups, the Boutet de Monvel calculus. A broad spectrum of readers will easily appreciate the stochastic intuition that this edition conveys. In fact, the book will provide a solid foundation for both researchers and graduate students in pure and applied mathematics interested in functional analysis, partial differential equations, Markov processes and the theory of pseudo-differential operators, a modern version of the classical potential theory.
Author : Jerome Goldstein,Neil Gretsky,John Uhl
Publisher : CRC Press
Page : 300 pages
File Size : 50,5 Mb
Release : 2020-09-23
Category : Mathematics
ISBN : 9781000148633
"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."
Author : Kazuaki Taira
Publisher : Springer Science & Business Media
Page : 196 pages
File Size : 43,6 Mb
Release : 2009-06-30
Category : Mathematics
ISBN : 9783642016769
This is a thorough and accessible exposition on the functional analytic approach to the problem of construction of Markov processes with Ventcel’ boundary conditions in probability theory. It presents new developments in the theory of singular integrals.
Author : Randall J. Swift,Alan Krinik,Jennifer M. Switkes,Jason H. Park
Publisher : American Mathematical Society
Page : 248 pages
File Size : 42,5 Mb
Release : 2021-11-22
Category : Mathematics
ISBN : 9781470459826
This volume contains the proceedings of the AMS Special Session on Celebrating M. M. Rao's Many Mathematical Contributions as he Turns 90 Years Old, held from November 9–10, 2019, at the University of California, Riverside, California. The articles show the effectiveness of abstract analysis for solving fundamental problems of stochastic theory, specifically the use of functional analytic methods for elucidating stochastic processes and their applications. The volume also includes a biography of M. M. Rao and the list of his publications.
Author : Kazuaki Taira
Publisher : Springer Nature
Page : 792 pages
File Size : 44,9 Mb
Release : 2022-05-28
Category : Mathematics
ISBN : 9789811910999
This book is an easy-to-read reference providing a link between functional analysis and diffusion processes. More precisely, the book takes readers to a mathematical crossroads of functional analysis (macroscopic approach), partial differential equations (mesoscopic approach), and probability (microscopic approach) via the mathematics needed for the hard parts of diffusion processes. This work brings these three fields of analysis together and provides a profound stochastic insight (microscopic approach) into the study of elliptic boundary value problems. The author does a massive study of diffusion processes from a broad perspective and explains mathematical matters in a more easily readable way than one usually would find. The book is amply illustrated; 14 tables and 141 figures are provided with appropriate captions in such a fashion that readers can easily understand powerful techniques of functional analysis for the study of diffusion processes in probability. The scope of the author’s work has been and continues to be powerful methods of functional analysis for future research of elliptic boundary value problems and Markov processes via semigroups. A broad spectrum of readers can appreciate easily and effectively the stochastic intuition that this book conveys. Furthermore, the book will serve as a sound basis both for researchers and for graduate students in pure and applied mathematics who are interested in a modern version of the classical potential theory and Markov processes. For advanced undergraduates working in functional analysis, partial differential equations, and probability, it provides an effective opening to these three interrelated fields of analysis. Beginning graduate students and mathematicians in the field looking for a coherent overview will find the book to be a helpful beginning. This work will be a major influence in a very broad field of study for a long time.
Author : Adam Bobrowski
Publisher : Cambridge University Press
Page : 279 pages
File Size : 47,5 Mb
Release : 2020-11-26
Category : Mathematics
ISBN : 9781108495790
A clear explanation of what an explosive Markov chain does after it passes through all available states in finite time.
Author : Niels Jacob
Publisher : Imperial College Press
Page : 504 pages
File Size : 51,7 Mb
Release : 2005
Category : Mathematics
ISBN : 9781860947155
This volume concentrates on how to construct a Markov process by starting with a suitable pseudo-differential operator. Feller processes, Hunt processes associated with Lp-sub-Markovian semigroups and processes constructed by using the Martingale problem are at the center of the considerations. The potential theory of these processes is further developed and applications are discussed. Due to the non-locality of the generators, the processes are jump processes and their relations to Levy processes are investigated. Special emphasis is given to the symbol of a process, a notion which generalizes that of the characteristic exponent of a Levy process and provides a natural link to pseudo-differential operator theory.
Author : Jerome Goldstein,Neil Gretsky,John Uhl
Publisher : CRC Press
Page : 296 pages
File Size : 42,5 Mb
Release : 2020-09-24
Category : Mathematics
ISBN : 9781000105421
"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."
Author : Adam Bobrowski
Publisher : Unknown
Page : 393 pages
File Size : 53,7 Mb
Release : 2005
Category : Functional analysis
ISBN : 0511198981
This text is designed both for students of probability and stochastic processes, and for students of functional analysis. Numerous standard and non-standard examples and exercises make it suitable for both a textbook for a course as well as for self-study.
Author : Niels Jacob
Publisher : World Scientific
Page : 517 pages
File Size : 52,9 Mb
Release : 2001-11-28
Category : Mathematics
ISBN : 9781783261345
After recalling essentials of analysis — including functional analysis, convexity, distribution theory and interpolation theory — this book handles two topics in detail: Fourier analysis, with emphasis on positivity and also on some function spaces and multiplier theorems; and one-parameter operator semigroups with emphasis on Feller semigroups and Lp-sub-Markovian semigroups. In addition, Dirichlet forms are treated. The book is self-contained and offers new material originated by the author and his students./a
Author : Niels Jacob
Publisher : World Scientific
Page : 528 pages
File Size : 53,6 Mb
Release : 2001
Category : Mathematics
ISBN : 1860949746
After recalling essentials of analysis OCo including functional analysis, convexity, distribution theory and interpolation theory OCo this book handles two topics in detail: Fourier analysis, with emphasis on positivity and also on some function spaces and multiplier theorems; and one-parameter operator semigroups with emphasis on Feller semigroups and Lp-sub-Markovian semigroups. In addition, Dirichlet forms are treated. The book is self-contained and offers new material originated by the author and his students. Sample Chapter(s). Introduction: Pseudo Differential Operators and Markov Processes (207 KB). Chapter 1: Introduction (190 KB). Contents: Essentials from Analysis: Calculus Results; Convexity; Some Interpolation Theory; Fourier Analysis and Convolution Semigroups: The PaleyOCoWienerOCoSchwartz Theorem; Bounded Borel Measures and Positive Definite Functions; Convolution Semigroups and Negative Definite Functions; The L(r)vyOCoKhinchin Formula for Continuous Negative Definite Functions; Bernstein Functions and Subordination of Convolution Semigroups; Fourier Multiplier Theorems; One Parameter Semigroups: Strongly Continuous Operator Semigroups; Subordination in the Sense of Bochner for Operator Semigroups; Generators of Feller Semigroups; Dirichlet Forms and Generators of Sub-Markovian Semigroups; and other papers. Readership: Graduate students, researchers and lecturers in analysis & differential equations, stochastics, probability & statistics, and mathematical physics."
Author : L. C. G. Rogers,David Williams
Publisher : Cambridge University Press
Page : 412 pages
File Size : 50,6 Mb
Release : 2000-04-13
Category : Mathematics
ISBN : 0521775949
Now available in paperback for the first time; essential reading for all students of probability theory.