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- W4306158378 abstract "We formulate a trajectorial version of the relative entropy dissipation identity for McKean–Vlasov diffusions, extending recent results which apply to non-interacting diffusions. Our stochastic analysis approach is based on time-reversal of diffusions and Lions’ differential calculus over Wasserstein space. It allows us to compute explicitly the rate of relative entropy dissipation along every trajectory of the underlying diffusion via the semimartingale decomposition of the corresponding relative entropy process. As a first application, we obtain a new interpretation of the gradient flow structure for the granular media equation, generalizing a formulation developed recently for the linear Fokker–Planck equation. Secondly, we show how the trajectorial approach leads to a new derivation of the HWBI inequality, which relates relative entropy (H), Wasserstein distance (W), barycenter (B) and Fisher information (I)." @default.
- W4306158378 created "2022-10-14" @default.
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- W4306158378 date "2023-02-01" @default.
- W4306158378 modified "2023-10-17" @default.
- W4306158378 title "A trajectorial approach to relative entropy dissipation of McKean–Vlasov diffusions: Gradient flows and HWBI inequalities" @default.
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- W4306158378 doi "https://doi.org/10.3150/22-bej1476" @default.
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