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Stochastic integrals for spde's: a comparison

Presented by: 
R Dalang [EPFL]
Tuesday 29th June 2010 - 11:30 to 12:20
INI Seminar Room 1
We present the Walsh theory of stochastic integrals with respect to martingale measures, and various extensions if this theory, alongside of the Da Prato and Zabczyk theory of stochastic integrals with respect to Hilbert-space-valued Wiener processes, and we explore the links between these theories. Somewhat surprisingly, the end results of both theories turn out to be essentially equivalent. We then show how each theory can be used to study stochastic partial differential equations, with an emphasis on the stochastic heat and wave equations driven by spatially homogeneous Gaussian noise that is white in time. We compare the solutions produced by the different theories. Authors: Robert Dalang (Ecole Polytechnique Fédérale de Lausanne), Lluis Quer-Sardanyons (Universitat Autònoma de Barcelona)

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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons