Particle approximation for a conditional McKean--Vlasov stochastic differential equation
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911814042779648 |
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| author | Du, Kai Li, Yunzhang Ye, Yuyang |
| author_facet | Du, Kai Li, Yunzhang Ye, Yuyang |
| contents | In this paper, we construct a type of interacting particle systems to approximate a class of stochastic different equations whose coefficients depend on the conditional probability distributions of the processes given partial observations. After proving the well-posedness and regularity of the particle systems, we establish a quantitative convergence result for the empirical measures of the particle systems in the Wasserstein space, as the number of particles increases. Moreover, we discuss an Euler--Maruyama scheme of the particle system and validate its strong convergence. A numerical experiment is conducted to illustrate our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17555 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Particle approximation for a conditional McKean--Vlasov stochastic differential equation Du, Kai Li, Yunzhang Ye, Yuyang Probability In this paper, we construct a type of interacting particle systems to approximate a class of stochastic different equations whose coefficients depend on the conditional probability distributions of the processes given partial observations. After proving the well-posedness and regularity of the particle systems, we establish a quantitative convergence result for the empirical measures of the particle systems in the Wasserstein space, as the number of particles increases. Moreover, we discuss an Euler--Maruyama scheme of the particle system and validate its strong convergence. A numerical experiment is conducted to illustrate our results. |
| title | Particle approximation for a conditional McKean--Vlasov stochastic differential equation |
| topic | Probability |
| url | https://arxiv.org/abs/2403.17555 |