Approximation of Invariant Measures for Stochastic Differential Equations with Piecewise Continuous Arguments via Backward Euler Method
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2019
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| Acceso en línea: | |
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| _version_ | 1866916403394641920 |
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| author | Chen, Chuchu Hong, Jialin Lu, Yulan |
| author_facet | Chen, Chuchu Hong, Jialin Lu, Yulan |
| contents | For the stochastic differential equation (SDE) which has piecewise continuous arguments (PCAs), is driven by multiplicative noises and its drift coefficients are dissipative, we show that the solution at integer time is a Markov chain and admits a unique invariant measure. In order to inherit numerically the invariant measure of SDE with PCAs, we apply the backward Euler (BE) method to the equation, and prove that the numerical solution at integer time is not only Markovian but also reproduces a unique numerical invariant measure. We present the time-independent weak error analysis for the method under certain hypothesis. Further, we show that the numerical invariant measure converges to the original one with order 1. Numerical experiments verify the theoretical analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1906_04096 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Approximation of Invariant Measures for Stochastic Differential Equations with Piecewise Continuous Arguments via Backward Euler Method Chen, Chuchu Hong, Jialin Lu, Yulan Numerical Analysis 60H35, 37M25, 65C30 For the stochastic differential equation (SDE) which has piecewise continuous arguments (PCAs), is driven by multiplicative noises and its drift coefficients are dissipative, we show that the solution at integer time is a Markov chain and admits a unique invariant measure. In order to inherit numerically the invariant measure of SDE with PCAs, we apply the backward Euler (BE) method to the equation, and prove that the numerical solution at integer time is not only Markovian but also reproduces a unique numerical invariant measure. We present the time-independent weak error analysis for the method under certain hypothesis. Further, we show that the numerical invariant measure converges to the original one with order 1. Numerical experiments verify the theoretical analysis. |
| title | Approximation of Invariant Measures for Stochastic Differential Equations with Piecewise Continuous Arguments via Backward Euler Method |
| topic | Numerical Analysis 60H35, 37M25, 65C30 |
| url | https://arxiv.org/abs/1906.04096 |