No Access

Stochastic Differential Equations in White Noise Space

H.-H. Kuo and
J. Xiong

H.-H. Kuo

Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA

Research supported by U.S. Army Research Office grant #DAAH04-94-G-0249.

Search for more papers by this author

and

J. Xiong

Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA

Search for more papers by this author

https://doi.org/10.1142/S0219025798000338Cited by:1 (Source: Crossref)

Abstract

We study infinite dimensional stochastic differential equations taking values in a white noise space. We show that under certain assumptions the distribution laws of the solution of such an equation induce generalized functions. The white noise integral equation satisfied by these generalized functions is derived. We apply the results to study the stochastic fluctuation of a two-dimensional neuron.