A convergent numerical algorithm for the stochastic growth-fragmentation problem
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866912381661085696 |
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| author | Wu, Dawei Zhou, Zhennan |
| author_facet | Wu, Dawei Zhou, Zhennan |
| contents | The stochastic growth-fragmentation model describes the temporal evolution of a structured cell population through a discrete-time and continuous-state Markov chain. The simulations of this stochastic process and its invariant measure are of interest. In this paper, we propose a numerical scheme for both the simulation of the process and the computation of the invariant measure, and show that under appropriate assumptions, the numerical chain converges to the continuous growth-fragmentation chain with an explicit error bound. With a triangle inequality argument, we are also able to quantitatively estimate the distance between the invariant measures of these two Markov chains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_09091 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A convergent numerical algorithm for the stochastic growth-fragmentation problem Wu, Dawei Zhou, Zhennan Numerical Analysis 37A50, 60J22, 65C40, 37N25 The stochastic growth-fragmentation model describes the temporal evolution of a structured cell population through a discrete-time and continuous-state Markov chain. The simulations of this stochastic process and its invariant measure are of interest. In this paper, we propose a numerical scheme for both the simulation of the process and the computation of the invariant measure, and show that under appropriate assumptions, the numerical chain converges to the continuous growth-fragmentation chain with an explicit error bound. With a triangle inequality argument, we are also able to quantitatively estimate the distance between the invariant measures of these two Markov chains. |
| title | A convergent numerical algorithm for the stochastic growth-fragmentation problem |
| topic | Numerical Analysis 37A50, 60J22, 65C40, 37N25 |
| url | https://arxiv.org/abs/2212.09091 |