Convergence rates of the splitting scheme for parabolic linear stochastic Cauchy problems

Details Convergence rates of the splitting scheme for parabolic linear stochastic Cauchy problems Convergence rates of the splitting scheme for parabolic linear stochastic Cauchy problems

2009-06-11

arxiv.org/abs/0906.2129v2

Mathematics

Numerical Analysis

Final version, to appear in SINUM

Scientific paper

We study the splitting scheme associated with the linear stochastic Cauchy problem dU(t) = AU(t) dt + dW(t), where A is the generator of an analytic C_0-semigroup S={S(t)} on a Banach space E and W={W(t)} is a Brownian motion with values in a fractional domain space E_\b associated with A. We prove that if \a,\b,\g,\th \ge 0 are such that \g + \th < 1 and max[0,(\a-\b+\th)] + \g < 1/2, then the approximate solutions U_n (where n is the number of time steps) converge to the solution U in the Holder space C^\g([0,T];E_\a), both in L^p-means and almost surely, with rate 1/n^\th.

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