Wong-Zakai type convergence in infinite dimensions

Details Wong-Zakai type convergence in infinite dimensions Wong-Zakai type convergence in infinite dimensions

2011-11-25

arxiv.org/abs/1111.6114v1

Mathematics

Probability

36 pages

Scientific paper

The paper deals with convergence of solutions of a class of stochastic differential equations driven by infinite-dimensional semimartingales. The infinite-dimensional semimartingales considered in the paper are Hilbert-space valued. The theorems presented generalize the convergence result obtained by Wong and Zakai for stochastic differential equations driven by linear interpolations of a finite-dimensional Brownian motion. In particular, a general form of the correction factor is derived. Examples are given illustrating the use of the theorems to obtain other kinds of approximation results.

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