Sample-path large deviations for a class of heavy-tailed Markov-additive processes

Abstract

For a class of additive processes driven by the affine recursion $X_{n+1}=A_{n+1}{X}_n+B_{n+1}$, we develop a sample-path large deviations principle in the $M_1^{\prime }$ topology on $\mathbb{D}[0,1]$. We allow $B_n$ to have both signs and focus on the case where Kesten’s condition holds on $A_1$, leading to heavy-tailed distributions. The most likely paths in our large deviations results are step functions with both positive and negative jumps.