GEOMETRIC AND SUBGEOMETRIC RATES FOR MARK OVIAN PROCESSES IN THE NEIGHBORHOOD OF LINEARITY

This paper is devoted to some models with a state space representation (1). Foster-Lyapounov type inequalities due to Tweedle [11], Tuominen and Tweedle [10] describe the conditions under which such a model rem ains ergodic. The applications are twofold. In the first case we exami ne an autoregressive model which departs from linearity additively. In the second case, the slate space model arises from a sublinear model. In each case conditions that ensure ergodicity are given, with geomet ric or, possibly, subgeometric rates of convergence to the ergodic mea sure.