Random additive perturbation of a $k$ term recurrence relation

Abstract

We are interested in stochastic processes satisfying a nonlinear recurrence relation of the form $$X_{n+k}=\hat{I}{¦}_0(X_n,...,X_{n+k-1})+\hat{I}{˜}_n$$ where $\hat{I}˜$ is a noise term. We establish the existence of an invariant measure for this process under given sufficient conditions on $\hat{I}{¦}_0.$

This work is a continuation of a previous paper on this problem (arXiv:1606.01644)