The Ito-Clifford integral II-stochastic differential equations

by C. Barnett, R. F. Streater and I. F. Wilde; J. London Math. Soc., 27, 373-384, 1983.

ABSTRACT

Let W_t be a Fermion martingale. It is shown that a stochastic differential equation of the form

dX_t=F(X_t,t)dW_t+dW_tG(X_t,t)+H(W_t,t)dt

has a unique solution in the L^2-space of the Clifford algebra for any initial condition provided that F,G,H satisfy a Lipschitz condition. Examples of such Lipschitz maps are considered. It is further shown that the solution is stable with respect to changes in the initial condition, and in the coefficients F,G,H.