Results are presented on the stability of solutions of stochastic delay differential equations with multiplicative noise and of convergent numerical solutions obtained by a a method of Euler-Maruyama type. An attempt is made to provide a fairly self-contained presentation. A basic concept of the...

Financial models consider often stochastic processes satisfying certain differential equations. We show that the solution of a particular geometric Brownian motion observed in discrete time is asymptotically equivalent with a Gaussian white noise model.