A Semigroup Point Of View On Splitting Schemes For Stochastic (Partial) Differential Equations

We construct normed spaces of real-valued functions with controlled growth on possibly infinite-dimensional state spaces such that semigroups of positive, bounded operators $(P_t{)}_{t\ge 0}$ thereon with ${\lim }_{t\to 0+}{P}_{t}f(x)=f(x)$ are in fact strongly continuous. This result applies to prove optimal rates of convergence of splitting schemes for stochastic (partial) differential equations with linearly growing characteristics and for sets of functions with controlled growth. Applications are general Da Prato-Zabczyk type equations and the HJM equations from interest rate theory.