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Abstract: We present the Walsh theory of stochastic integrals with respect tomartingale measures, alongside of the Da Prato and Zabczyk theory of stochasticintegrals with respect to Hilbert-space-valued Wiener processes and some otherapproaches to stochastic integration, and we explore the links between thesetheories. We then show how each theory can be used to study stochastic partialdifferential equations, with an emphasis on the stochastic heat and waveequations driven by spatially homogeneous Gaussian noise that is white in time.We compare the solutions produced by the different theories.

Autor: Robert C. Dalang, Lluis Quer-Sardanyons


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