Abstract:
In the paper, we consider a model of random recurrent sequences with cooling. Let $\boldsymbol{\tau} = \{\tau_i\,|\, \tau_i \in \mathbb{N}\}_{i=1}^\infty$ be a deterministic bounded sequence of cooling durations, $k(n) = \min \{j \colon \tau_1 + \dotsb + \tau_{j} \geqslant n\}$ be the cooling number at the $n$-th step. Let $\xi_i$, $i\geqslant 1$, be independent identically distributed non-lattice random variables. We define a recurrent sequence with cooling by a random equation $Y_n = A_n Y_{n-1} + B_n$, $n\geqslant 1$, where $A_n = \exp \left(\xi_{k(n)}\right)$ and the random variables $B_n$ satisfy some moment assumptions.
Keywords:associated random walk, random recurrent sequences, large deviations.
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