Quasi-ergodic theorems for Feynman-Kac semigroups and large deviation for additive functionals
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915709092626432 |
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| author | Kim, Daehong Tagawa, Takara Velleret, Aurélien |
| author_facet | Kim, Daehong Tagawa, Takara Velleret, Aurélien |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_17997 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quasi-ergodic theorems for Feynman-Kac semigroups and large deviation for additive functionals Kim, Daehong Tagawa, Takara Velleret, Aurélien Probability 37A30, 60J45 (Primary), 60G52, 47D06, 60J46 (Secondary) G.3 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. |
| title | Quasi-ergodic theorems for Feynman-Kac semigroups and large deviation for additive functionals |
| topic | Probability 37A30, 60J45 (Primary), 60G52, 47D06, 60J46 (Secondary) G.3 |
| url | https://arxiv.org/abs/2401.17997 |