On the Cauchy problem for parabolic SPDEs in Hölder classes

R. Mikulevicius

doi:10.1214/aop/1019160112

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Home > Journals > Ann. Probab. > Volume 28 > Issue 1 > Article

January 2000 On the Cauchy problem for parabolic SPDEs in Hölder classes

R. Mikulevicius

Ann. Probab. 28(1): 74-103 (January 2000). DOI: 10.1214/aop/1019160112

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Abstract

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.

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R. Mikulevicius. "On the Cauchy problem for parabolic SPDEs in Hölder classes." Ann. Probab. 28 (1) 74 - 103, January 2000. https://doi.org/10.1214/aop/1019160112