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 $X_{n+1}=A_n{X}_n+B_n$, we develop a sample-path large deviations principle in the $M_1^{\prime }$ topology on $D[0,1]$. 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.

Preprint: comments are welcome

References in corpus (2)

• Extremal behavior of stochastic integrals driven by regularly varying Lévy processes
• A large deviations approach to limit theory for heavy-tailed time series