Stochastic Partial Differential Equations with Lévy Noise: An Evolution Equation Approach

Przednia okładka
Cambridge University Press, 11 paź 2007 - 419
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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 appeared here for the first time in book form. 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.
 

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Spis treści

Why equations with Levy noise?
3
Analytic preliminaries
13
Probabilistic preliminaries
20
4Levy processes
38
5Levy semigroups
75
Poisson random measures
83
Cylindrical processes and reproducing kernels
91
Stochastic integration
107
Stochastic parabolic problems
201
Wave and delay equations
225
Equations driven by a spatially homogeneous noise
240
Equations with noise on the boundary
272
Invariant measures
287
Lattice systems
299
Stochastic Burgers equation
312
Environmental pollution model
322

General existence and uniqueness results
139
Equations with nonLipschitz coefficients
179
Factorization and regularity
190

Kluczowe wyrazy i wyrażenia

Informacje o autorze (2007)

Szymon Peszat is an Associate Professor in the Institute of Mathematics at the Polish Academy of Sciences.

Jerzy Zabczyk is a Professor in the Institute of Mathematics at the Polish Academy of Sciences. He is the author (with G. Da Prato) of three earlier books for Cambridge University Press: Stochastic Equations in Infinite Dimensions (1992), Ergodicity for Infinite Dimensional Systems (1996) and Second Order Partial Differential Equations (2002).

Informacje bibliograficzne