Tail behaviour of the stationary density of general non-linear autoregressive processes of order 1

We examine the main properties of the Markov chain X t = T ( X t – 1 ) + σ( X t – 1 ) ε t . Under general and tractable assumptions, we derive bounds for the tails of the stationary density of the process { X t } in terms of the common density of the ε t 's.