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Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 52,8 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9781783260249
Author : Niels Jacob
Publisher : Imperial College Press
Page : 504 pages
File Size : 45,9 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 : Niels Jacob
Publisher : Imperial College Press
Page : 506 pages
File Size : 52,7 Mb
Release : 2001
Category : Mathematics
ISBN : 9781860945687
This work covers 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.
Author : Niels Jacob
Publisher : De Gruyter Akademie Forschung
Page : 218 pages
File Size : 51,7 Mb
Release : 1996
Category : Mathematics
ISBN : UOM:39015040997887
Author : Niels Jacob
Publisher : World Scientific
Page : 528 pages
File Size : 55,8 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 : Niels Jacob
Publisher : World Scientific
Page : 517 pages
File Size : 46,6 Mb
Release : 2001
Category : Mathematics
ISBN : 9781860942938
This work covers 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.
Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 42,5 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9781783261208
Author : Jacob
Publisher : Unknown
Page : 208 pages
File Size : 55,5 Mb
Release : 1996-06-01
Category : Electronic
ISBN : 3527400982
Author : Niels Jacob
Publisher : Unknown
Page : 128 pages
File Size : 47,5 Mb
Release : 2001
Category : Dirichlet forms
ISBN : 1860942938
This work covers 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.
Author : Kazuaki Taira
Publisher : Springer Science & Business Media
Page : 196 pages
File Size : 43,8 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 : Niels Jacob
Publisher : World Scientific
Page : 517 pages
File Size : 44,7 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 : Mark I. Freidlin
Publisher : Springer Science & Business Media
Page : 168 pages
File Size : 49,7 Mb
Release : 1996-03-28
Category : Mathematics
ISBN : 3764353929
Probabilistic methods can be applied very successfully to a number of asymptotic problems for second-order linear and non-linear partial differential equations. Due to the close connection between the second order differential operators with a non-negative characteristic form on the one hand and Markov processes on the other, many problems in PDE's can be reformulated as problems for corresponding stochastic processes and vice versa. In the present book four classes of problems are considered: - the Dirichlet problem with a small parameter in higher derivatives for differential equations and systems - the averaging principle for stochastic processes and PDE's - homogenization in PDE's and in stochastic processes - wave front propagation for semilinear differential equations and systems. From the probabilistic point of view, the first two topics concern random perturbations of dynamical systems. The third topic, homog- enization, is a natural problem for stochastic processes as well as for PDE's. Wave fronts in semilinear PDE's are interesting examples of pattern formation in reaction-diffusion equations. The text presents new results in probability theory and their applica- tion to the above problems. Various examples help the reader to understand the effects. Prerequisites are knowledge in probability theory and in partial differential equations.
Author : Shahla Molahajloo,M. W. Wong
Publisher : Springer
Page : 257 pages
File Size : 42,5 Mb
Release : 2019-05-08
Category : Mathematics
ISBN : 9783030051686
This volume, like its predecessors, is based on the special session on pseudo-differential operators, one of the many special sessions at the 11th ISAAC Congress, held at Linnaeus University in Sweden on August 14-18, 2017. It includes research papers presented at the session and invited papers by experts in fields that involve pseudo-differential operators. The first four chapters focus on the functional analysis of pseudo-differential operators on a spectrum of settings from Z to Rn to compact groups. Chapters 5 and 6 discuss operators on Lie groups and manifolds with edge, while the following two chapters cover topics related to probabilities. The final chapters then address topics in differential equations.
Author : Paolo Boggiatto,Luigi Rodino,Joachim Toft,M. W. Wong
Publisher : Birkhäuser
Page : 244 pages
File Size : 44,7 Mb
Release : 2006-01-19
Category : Mathematics
ISBN : 3764375132
Author : Kazuaki Taira
Publisher : Unknown
Page : 502 pages
File Size : 51,5 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.
