Pseudo Differential Operators & Markov Processes
Pseudo Differential Operators & Markov Processes

Author: Niels Jacob

Publisher: Imperial College Press

Published: 2005

Total Pages: 504

ISBN-13: 1860947158

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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.

Pseudo Differential Operators & Markov Processes: Markov processes and applications
Pseudo Differential Operators & Markov Processes: Markov processes and applications

Author: Niels Jacob

Publisher: Imperial College Press

Published: 2001

Total Pages: 506

ISBN-13: 1860945686

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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.

Pseudo Differential Operators and Markov Processes
Pseudo Differential Operators and Markov Processes

Author: Niels Jacob

Publisher: World Scientific

Published: 2001

Total Pages: 528

ISBN-13: 9781860949746

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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."

Pseudo Differential Operators And Markov Processes, Volume I: Fourier Analysis And Semigroups
Pseudo Differential Operators And Markov Processes, Volume I: Fourier Analysis And Semigroups

Author: Niels Jacob

Publisher: World Scientific

Published: 2001-11-28

Total Pages: 517

ISBN-13: 178326134X

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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

Pseudo Differential Operators And Markov Processes, Volume Ii: Generators And Their Potential Theory
Pseudo Differential Operators And Markov Processes, Volume Ii: Generators And Their Potential Theory

Author: Niels Jacob

Publisher: World Scientific

Published: 2002-07-19

Total Pages: 477

ISBN-13: 178326120X

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In this volume two topics are discussed: the construction of Feller and Lp-sub-Markovian semigroups by starting with a pseudo-differential operator, and the potential theory of these semigroups and their generators. The first part of the text essentially discusses the analysis of pseudo-differential operators with negative definite symbols and develops a symbolic calculus; in addition, it deals with special approaches, such as subordination in the sense of Bochner. The second part handles capacities, function spaces associated with continuous negative definite functions, Lp -sub-Markovian semigroups in their associated Bessel potential spaces, Stein's Littlewood-Paley theory, global properties of Lp-sub-Markovian semigroups, and estimates for transition functions.

Boundary Value Problems and Markov Processes
Boundary Value Problems and Markov Processes

Author: Kazuaki Taira

Publisher: Springer

Published: 2009-06-17

Total Pages: 196

ISBN-13: 3642016774

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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.