, Volume 25, Issue 1, pp 81-106

Approximation of some stochastic differential equations by the splitting up method

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Abstract

In this paper we deal with the convergence of some iterative schemes suggested by Lie-Trotter product formulas for stochastic differential equations of parabolic type. The stochastic equation is split into two problems which are simpler for numerical computations, as already shown, for example, for the Zakaï equation. An estimate of the approximation error is given in a particular case.

The work of A. Bensoussan and R. Glowinski was supported by the U.S. Army Research Office under Contract DAAL03-86-K-0138. Additional support was given by NSF via Grant INT-8612680.