Stochastic partial differential equations (Q2873807)

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scientific article; zbMATH DE number 6250568
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Stochastic partial differential equations
scientific article; zbMATH DE number 6250568

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    27 January 2014
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    stochastic partial differential equations
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    Lévy-type noise
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    stochastic integrals
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    Poisson random fields
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    mild solutions
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    asymptotic behaviour
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    population models
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    random environments
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    financial mathematics
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    Stochastic partial differential equations (English)
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    This is the second edition of the very well written and introductory, application-oriented book on stochastic partial differential equations (SPDEs) by P. L. Chow. Compared to the first edition [Zbl 1134.60043], the main change is adding new materials about SPDEs driven by Lévy-type noise. In Chapter 1, two sections on stochastic integrals with respect to Poisson random fields and stochastic differential equations of Lévy-type are new. Chapter 3 contains the most changes in this regard: solution of stochastic heat equation with Poisson noise, existence and regularity of mild solutions to linear equations with additive noise and the last section on nonlinear parabolic equations with Lévy-type noise. Moreover, in Chapters 5 and 6, the author considers the linear and semilinear wave equations driven by Poisson-type noises and Poisson stochastic integrals in Hilbert spaces with an analysis of mild solutions to Poisson stochastic evolution equations. The theory discussed in the previous chapters is employed in Chapter 8 to study some examples and applications. Specifically, two sections on population growth models in random environments and financial mathematics are added to this chapter.
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