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.
"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