Random additive perturbation of a $k$ term recurrence relation

Lisette Jager, Killian Verdure

We are interested in stochastic processes satisfying a nonlinear recurrence relation of the form $$X_{n+k}={\Phi }_0(X_n,...,X_{n+k-1})+{\Theta }_n$$ where $\Theta$ is a noise term. We e…