For a class of additive processes driven by the affine recursion Xn+1 = An+1Xn+Bn+1, we develop a sample-path large deviations principle in the M′1 topology on D[0, 1]. We allow Bn 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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Electronic Journal of Probability
Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands

Chen, B., Rhee, C.-H., & Zwart, B. (2024). Sample-path large deviations for a class of heavy-tailed Markov-additive processes. Electronic Journal of Probability, 29, 53:1–53:44. doi:10.1214/24-EJP1115