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Encyclopedia of Mathematics and Its Applications #113: Stochastic Partial Differential Equations with Levy Noise: An Evolution Equation Approach

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Encyclopedia of Mathematics and Its Applications #113: Stochastic Partial Differential Equations with Levy Noise: An Evolution Equation Approach Cover

 

Synopses & Reviews

Publisher Comments:

Recent years have seen an explosion of interest in stochastic partial differential equations where the driving noise is discontinuous. In this comprehensive monograph, two leading experts detail the evolution equation approach to their solution. Most of the results appear here for the first time in book form, and the volume is sure to stimulate further research in this important field. The authors start with a detailed analysis of Lévy processes in infinite dimensions and their reproducing kernel Hilbert spaces; cylindrical Lévy processes are constructed in terms of Poisson random measures; stochastic integrals are introduced. Stochastic parabolic and hyperbolic equations on domains of arbitrary dimensions are studied, and applications to statistical and fluid mechanics and to finance are also investigated. Ideal for researchers and graduate students in stochastic processes and partial differential equations, this self-contained text will also interest those working on stochastic modeling in finance, statistical physics and environmental science.

Book News Annotation:

Peszat and Zabczyk (both are in the department of mathematics of the Polish Academy of Sciences) offer an important contribution to the literature on stochastic processes that will be of interest to graduate students and researchers. Their theory builds on the results of equations driven by Wiener processes and results of both Lvy and Wiener noise are discussed in tandem. Eight initial chapters provide a foundation to the theory that follows, with discussion that includes the basis of equations with Lvy noise, probability theory with martingales, Lvy processes and semigroups, cylindrical processes and reproducing kernels, and stochastic integration. Existence and regularity are explored in chapters that examine wave and delay equations, equations driven by spatially homogeneous noise, and equations with noise on the boundary, among other topics. The theory is then applied, in five chapters on invariant measures, Lattice systems, stochastic Burgers equation, an environmental pollution model, and in six bond market models. Several appendices provide a number of related proofs and results. A list of symbols is provided. Annotation ©2008 Book News, Inc., Portland, OR (booknews.com)

Product Details

ISBN:
9780521879897
Author:
Peszat, S.
Publisher:
Cambridge University Press
Author:
Zabczyk, J.
Subject:
Differential Equations
Subject:
Stochastic partial differential equations
Subject:
Lâevy processes.
Subject:
Mathematics-Differential Equations
Series:
Encyclopedia of Mathematics and Its Applications
Series Volume:
113
Publication Date:
20071131
Binding:
Hardcover
Language:
English
Illustrations:
Y
Pages:
419
Dimensions:
9.27x6.48x1.14 in. 1.72 lbs.

Related Subjects

Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Differential Equations

Encyclopedia of Mathematics and Its Applications #113: Stochastic Partial Differential Equations with Levy Noise: An Evolution Equation Approach New Hardcover
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