Robert C. Dalang, Lluis Quer-Sardanyons
Published 2010-01-06Version 1
We present the Walsh theory of stochastic integrals with respect to martingale measures, alongside of the Da Prato and Zabczyk theory of stochastic integrals with respect to Hilbert-space-valued Wiener processes and some other approaches to stochastic integration, and we explore the links between these theories. 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.
A note on stochastic integrals as $L^2$-curves
Sharp supremum and Hölder bounds for stochastic integrals indexed by a parameter
Stochastic integrals and BDG's inequalities in Orlicz-type spaces
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