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On the Cauchy problem for parabolic SPDEs in Hölder classes. (English) Zbl 1044.60050

Summary: We study Cauchy’s problem for certain second-order linear parabolic stochastic differential equation (SPDE) 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.

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
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References:

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