On Cauchy-Dirichlet problem in half-space for parabolic SPDEs in weighted Hölder spaces

R. Mikulevicius and H. Pragarauskas

Stochastic Processes and their Applications, 2003, vol. 106, issue 2, 185-222

Abstract: We study the Cauchy-Dirichlet problem for a second-order linear parabolic stochastic differential equation in the half-space with a zero-order noise term driven by a cylindrical Brownian motion. Considering its solution as a function with values in a probability space and using the methods of deterministic partial differential equations, we establish the existence and uniqueness of a strong solution in Hölder classes with weights.

Keywords: Parabolic; stochastic; partial; differential; equations; Cauchy-Dirichlet; problem; Schauder; apriori; estimates; weighted; Holder; spaces (search for similar items in EconPapers)
Date: 2003
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