P. Dörsek, J. Teichmann:

"A semigroup point of view on splitting schemes for stochastic (partial) differential equations";

in: "ASC Report 28/2010", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2010, ISBN: 978-3-902627-03-2.

We construct normed spaces of real-valued functions with controlled

growth on possibly infinite-dimensional state spaces such that semigroups

of positive, bounded operators (Pt)t≥0 thereon with limt→0+ Ptf(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.

http://www.asc.tuwien.ac.at/preprint/2010/asc28x2010.pdf

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