Multiplicative ergodicity of Laplace transforms for additive functional of Markov chains

2015/06/25 by Loı̈c Hervé, Loïc Hervé, Hervé, Loïc +2
Business, Management and Accounting · Engineering · Mathematics · #Advanced Queuing Theory Analysis #FOS: Mathematics #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stability and Control of Uncertain Systems #math.PR

paper · pdf · doi:10.48550/arxiv.1506.07659

openalex publication_date 2015/06/25 · arxiv created 2015/09/10 · arxiv updated 2015/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study properties of the Laplace transforms of non-negative additive functionals of Markov chains. We are namely interested in a multiplicative ergodicity property used in [18] to study bifurcating processes with ancestral dependence. We develop a general approach based on the use of the operator perturbation method. We apply our general results to two examples of Markov chains, including a linear autoregressive model. In these two examples the operator-type assumptions reduce to some expected finite moment conditions on the functional (no exponential moment conditions are assumed in this work).

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