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

2020/10/21 by Chen, Bohan, Rhee, Chang-Han, Zwart, Bert · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2010.10751

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 M₁' topology on D [0,1]. We allow B_n to have both signs and focus on the case where Kesten's condition holds on A₁, leading to heavy-tailed distributions. The most likely paths in our large deviations results are step functions with both positive and negative jumps.

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