The Existence of a Unique Invariant Probability Measure for a Markov Process $X_{n+1}=f(X_n)+varepsilon_{n+1}$

We consider a Markov proces ${X_n} on [0,\infty)^k$ which is generated by $X_{n+1} = f(X_n) + \varepsilon_{n+1}$ where f is a continuous, nondecreasing concave function. Sufficient conditions for the existence of a unique invariant probability measure for ${X_n}$ are obtained.