Author

A. Aliev

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Open access Nov 2026

Exact variational cost for small-noise exit time in a two-slope autoregressive model

We determine the quadratic variational cost that yields the large-deviation upper bound for the mean exit time from $(-1,1)$ in the small-noise regime for an autoregressive process driven by a continuous two-slope map f lying strictly below the diagonal on $(0,1)$. The Klebaner–Liptser reduction expresses this constant...

A. Aliev, A. Dzhalilov · Modern Stochastics: Theory a... · 0 citations

Open access Oct 2026

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...

A. Aliev, A. Dzhalilov, R. Fontana · Uzbek Mathematical Journal · 0 citations