Work

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

Year: 2024

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2401.17997

Authors: Kim, Daehong, Tagawa, Takara, Velleret, Aurélien

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

Award: Spectral theory of Schrodinger forms and Stochastic analysis for weighted Markov processes

OpenAlex ID: W4391463073

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