We consider the markov process ${X_n}$ on R which is genereated by $X_{n+1} = f(X_n) + \epsilon_{n+1}$. Sufficient conditions for irreducibility and geometric ergodicity are obtained for such Markov processes. In additions, when ${X_n}$ is geometrica...
We consider the markov process ${X_n}$ on R which is genereated by $X_{n+1} = f(X_n) + \epsilon_{n+1}$. Sufficient conditions for irreducibility and geometric ergodicity are obtained for such Markov processes. In additions, when ${X_n}$ is geometrically ergodic, the functional central limit theorem is proved for every bounded functions on R.