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

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.