Perturbation theory for killed Markov processes and quasi-stationary distributions
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866908761758629888 |
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| author | Rudolf, Daniel Wang, Andi Q. |
| author_facet | Rudolf, Daniel Wang, Andi Q. |
| contents | Motivated by recent developments of quasi-stationary Monte Carlo methods, we investigate the stability of quasi-stationary distributions of killed Markov processes under perturbations of the generator. We first consider a general bounded self-adjoint perturbation operator, and after that, study a particular unbounded perturbation corresponding to truncation of the killing rate. In both scenarios, we quantify the difference between eigenfunctions of the smallest eigenvalue of the perturbed and unperturbed generators in a Hilbert space norm. As a consequence, L1 norm estimates of the difference of the resulting quasi-stationary distributions in terms of the perturbation are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_13819 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Perturbation theory for killed Markov processes and quasi-stationary distributions Rudolf, Daniel Wang, Andi Q. Probability Methodology 60J70, 47A55, 65C05, 60J22 Motivated by recent developments of quasi-stationary Monte Carlo methods, we investigate the stability of quasi-stationary distributions of killed Markov processes under perturbations of the generator. We first consider a general bounded self-adjoint perturbation operator, and after that, study a particular unbounded perturbation corresponding to truncation of the killing rate. In both scenarios, we quantify the difference between eigenfunctions of the smallest eigenvalue of the perturbed and unperturbed generators in a Hilbert space norm. As a consequence, L1 norm estimates of the difference of the resulting quasi-stationary distributions in terms of the perturbation are provided. |
| title | Perturbation theory for killed Markov processes and quasi-stationary distributions |
| topic | Probability Methodology 60J70, 47A55, 65C05, 60J22 |
| url | https://arxiv.org/abs/2109.13819 |