On the oscillation of solutions of stochastic difference equations

This paper considers the pathwise oscillatory behaviour of the scalar nonlinear stochastic difference equation X(n + 1) = X(n) - F(X(n)) + G(n,X(n))E(n + 1), n = 0, 1, . . . , with non-random initial value X0. Here (E(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.