Abstract / Description of output
In this short note, we establish Malliavin differentiability of McKean-Vlasov Stochastic Differential Equations (MV-SDEs) with drifts satisfying both a locally Lipschitz and a one-sided Lipschitz assumption, and where the diffusion coefficient is assumed to be uniformly Lipschitz in its variables.
As a secondary contribution, we investigate how Malliavin differentiability transfers across the interacting particle system associated with the McKean-Vlasov equation to its limiting equation. This final result requires both spatial and measure differentiability of the coefficients and doubles as a standalone result of independent interest since the study of Malliavin derivatives of weakly interacting particle systems seems novel to the literature. The presentation is didactic and finishes with a discussion on mollification techniques for the Lions derivative.
As a secondary contribution, we investigate how Malliavin differentiability transfers across the interacting particle system associated with the McKean-Vlasov equation to its limiting equation. This final result requires both spatial and measure differentiability of the coefficients and doubles as a standalone result of independent interest since the study of Malliavin derivatives of weakly interacting particle systems seems novel to the literature. The presentation is didactic and finishes with a discussion on mollification techniques for the Lions derivative.
Original language | English |
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Journal | Boletim da Sociedade Portuguesa de Matemática |
Publication status | Accepted/In press - 19 Aug 2024 |