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

Bohan Chen; Chang Han Rhee; Bert Zwart

doi:10.1214/24-EJP1115

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

Bohan Chen, Chang Han Rhee, Bert Zwart

Industrial Engineering and Management Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

For a class of additive processes driven by the affine recursion X_n+1 = An+1Xn+Bn+1, we develop a sample-path large deviations principle in the M^′1 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.

Original language	English (US)
Article number	53
Journal	Electronic Journal of Probability
Volume	29
DOIs	https://doi.org/10.1214/24-EJP1115
State	Published - 2024

Funding

*C.-H.R is supported by NSF Grant CMMI-2146530. †Munich Re, Germany. E-mail: [email protected] ‡Northwestern University, United States of America. E-mail: [email protected] §Centrum Wiskunde Informatica, The Netherlands. E-mail: [email protected]

Keywords

heavy tails
Markov additive process
power law
sample-path large deviations
stochastic recurrence equation

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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

Abstract

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Keywords

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