On the oscillation of solutions of stochastic difference equations.

Abstract

This paper considers the pathwise oscillatory behaviour of the scalar nonlinear stochastic dif- ference equation X(n + 1) = X(n) − F (X(n)) + G(n, X(n))ξ(n + 1), n = 0, 1, . . . , with non-random initial value X0 . Here (ξ(n))n≥0 is a sequence of independent random variables with zero mean and unit variance. The functions f : R → R and g : R → R are presumed to be continuous.