Titlebook: A Minicourse on Stochastic Partial Differential Equations; Robert Dalang,Davar Khoshnevisan,Yimin Xiao,Davar Book 2009 Springer-Verlag Be

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https://doi.org/10.1057/9781137340023eneral, and the stochastic heat equation, in particular. The chief aim here is to get to the heart of the matter quickly. We achieve this by studying a few concrete equations only. This chapter provides sufficient preparation for learning more advanced theory from the remainder of this volume.

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Leonardo M. Carneiro,Édison Vicente Oliveirariving noise is Gaussian, spatially homogeneous and white in time. We mainly address issues of existence, uniqueness and Hölder—Sobolev regularity. We also present an extension of Walsh‘s theory of stochastic integration with respect to martingale measures that is useful for spatial dimensions . ≥ 3

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Nilton C. Cáceres,Christopher R. Dickmanochastic partial differential equations. The Malliavin calculus is a differential calculus on a Gaussian space which has been developed from the probabilistic proof by Malliavin of H¨ormander‘s hypoellipticity theorem (see [8]). In the next section we present an introduction to the Malliavin calculu

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Leonardo M. Carneiro,Édison Vicente Oliveirascaling Gaussian fields with stationary increments, and the solution to the stochastic heat equation..This paper is concerned with sample path properties of anisotropic Gaussian random fields in general. Let . be a Gaussian random field with values in R. and with parameters H.,…,H.. Our goal is to c

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https://doi.org/10.1007/978-3-540-85994-9Geometric measure theory and fractals; Interacting particle systems; Malliavin calculus; Stochastic ana

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Nilton C. Cáceres,Christopher R. Dickmans, and we derive the main properties of the derivative and divergence operators. Section 3 is devoted to establish the main criteria for the existence and regularity of density for a random variable in a Gaussian space.