R. Fontana

Small-noise asymptotics of exit times for a class of nonlinear autoregressive processes

We study exit times from the interval $[-1,1]$ for the nonlinear autoregressive process given, for $n\geq 0$, by $$ X^{(\varepsilon)}_{n+1}(\varphi_{f,g}) =\varphi_{f,g}\bigl(X^{(\varepsilon)}_{n}\bigr)+\varepsilon\xi_{n+1}, $$ where $\varepsilon>0$ is a small noise parameter, $\{\xi_n\}$ is a sequence of independent s...