Quantitative weak propagation of chaos for McKean--Vlasov branching diffusion processes
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909988747739136 |
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| author | Cao, Wenjing Ren, Zhenjie Tan, Xiaolu |
| author_facet | Cao, Wenjing Ren, Zhenjie Tan, Xiaolu |
| contents | We study in this paper the weak propagation of chaos for McKean--Vlasov diffusions with branching, whose induced marginal measures are nonnegative finite measures but not necessary probability measures. The flow of marginal measures satisfies a non-linear Fokker--Planck equation, along which we provide a functional Itô's formula. We then consider a functional of the terminal marginal measure of the branching process, whose conditional value is solution to a Kolmogorov backward master equation. By using Itô's formula and based on the estimates of second-order linear and intrinsic functional derivatives of the value function, we finally derive a quantitative weak convergence rate for the empirical measures of the branching diffusion processes with finite population. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08330 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantitative weak propagation of chaos for McKean--Vlasov branching diffusion processes Cao, Wenjing Ren, Zhenjie Tan, Xiaolu Probability 60J80, 60H10 We study in this paper the weak propagation of chaos for McKean--Vlasov diffusions with branching, whose induced marginal measures are nonnegative finite measures but not necessary probability measures. The flow of marginal measures satisfies a non-linear Fokker--Planck equation, along which we provide a functional Itô's formula. We then consider a functional of the terminal marginal measure of the branching process, whose conditional value is solution to a Kolmogorov backward master equation. By using Itô's formula and based on the estimates of second-order linear and intrinsic functional derivatives of the value function, we finally derive a quantitative weak convergence rate for the empirical measures of the branching diffusion processes with finite population. |
| title | Quantitative weak propagation of chaos for McKean--Vlasov branching diffusion processes |
| topic | Probability 60J80, 60H10 |
| url | https://arxiv.org/abs/2601.08330 |