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

被引：1

作者：

Chen, Bohan ^{[1
]}

Rhee, Chang-Han ^{[2
]}

Zwart, Bert ^{[3
]}

机构：

[1] Munich Re, Munich, Germany

[2] Northwestern Univ, Evanston, IL USA

[3] Ctr Wiskunde Informat, Amsterdam, Netherlands

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2024年 / 29卷

基金：

美国国家科学基金会;

关键词：

sample-path large deviations; heavy tails; Markov additive process; stochastic recurrence equation; power law; RANDOM-WALKS; ASYMPTOTIC EVALUATION; PROCESS EXPECTATIONS; SPECTRAL THEORY; LIMIT-THEOREMS; LEVY PROCESSES; EQUATIONS; PROBABILITY; PRINCIPLE; QUEUES;

D O I：

10.1214/24-EJP1115

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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 M10 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.

引用

页数：44

共 38 条

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