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arXiv · 2401.17997

Quasi-ergodic theorems for Feynman-Kac semigroups and large deviation for additive functionals

Daehong Kim·Takara Tagawa·Aurélien Velleret
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Abstract

We study the long-time behavior of an additive functional that takes into account the jumps of a symmetric Markov process. This process is assumed to be observed through a biased observation scheme that includes the survival to events of extinction and the Feynman-Kac weight by another similar additive functional. Under conditioning for the convergence to a quasi-stationary distribution and for two-sided estimates of the Feynmac-Kac semigroup to be obtained, we shall discuss general assumptions on the symmetric Markov process. For the law of additive functionals, we will prove a quasi-ergodic theorem, namely a conditional version of the ergodic theorem and a conditional functional weak law of large numbers. As an application, we also establish a large deviation principle for the mean ratio of additive functionals.

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Daehong Kim, Takara Tagawa, Aurélien Velleret. 2026-01-06. Quasi-ergodic theorems for Feynman-Kac semigroups and large deviation for additive functionals. https://arxiv.org/abs/2401.17997

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