zbMATH — the first resource for mathematics

A convergence result for stochastic partial differential equations. (English) Zbl 0653.60049
It is shown that for regular approximations $$w_ n$$ of the Brownian motion w, the solutions of $du_ n-A u_ n dt+B u_ n dw_ n$ converge to the solution of the abstract Stratonovich stochastic differential equation $$du=A u dt+B u dw$$. The assumptions on the operators A and B permit physically reasonable applications, and some PDE examples are given.
Reviewer: T.C.Gard

MSC:
 60H15 Stochastic partial differential equations (aspects of stochastic analysis)
Full Text:
References:
 [1] Acquistapace P., An approach to Ito linear equations in Hilbert spaces by approximations of white noise with coloured noise, Preprint 42 · Zbl 0547.60066 [2] Batchelor G. K., The Theory of Homogenous Turbulence (1959) [3] DOI: 10.1512/iumj.1976.25.25049 · Zbl 0319.60038 · doi:10.1512/iumj.1976.25.25049 [4] Chow P. L., Probabilistic Analysis and Related Problems 1 (1978) [5] DOI: 10.1080/07362998308809004 · Zbl 0511.60055 · doi:10.1080/07362998308809004 [6] Daprato G., Stochastics 6 pp 105– (1982) [7] DOI: 10.1016/0022-247X(82)90041-5 · Zbl 0497.93055 · doi:10.1016/0022-247X(82)90041-5 [8] Ikeda N., Stochastic Differential Equations and Diffusion Processes (1981) · Zbl 0495.60005 [9] Lions J. L., Optimal Control of Systems Governed by Partial Differential Equations (1971) · Zbl 0203.09001 [10] Lions J. L., Non-homogenous Boundary Value Problems and Applications (1972) [11] Mcshane E. I., Stochastic Calculus and Stochastic Models (1974) · Zbl 0292.60090 [12] Pardoux E., C.R. Acad. Sc. Paris, t. 21 pp 101– (1972) [13] Pazy A. J., Semigroups of Bounded Linear Operators (1984) [14] DOI: 10.1214/aop/1176995608 · Zbl 0391.60056 · doi:10.1214/aop/1176995608 [15] Szafirski B., Bull. Acad. Polon. Sci. Ser. Math.Astron. Phys 19 pp 785– (1971) [16] DOI: 10.1214/aoms/1177699916 · Zbl 0138.11201 · doi:10.1214/aoms/1177699916 [17] Yosida K., Functional Analysis (1980) · Zbl 0435.46002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.