Nonlinear Vlasov-Fokker-Planck dynamics admit a GENERIC structure that reduces to a generalized Wasserstein gradient flow whose trajectorial dissipation captures the nonlinear interaction and whose partial degeneracy produces a metric decomposition supporting a partial HWI inequality.
Carmona,Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications.SIAM, Philadelphia, PA
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Nonlinear Vlasov-Fokker-Planck equations: From generalized Wasserstein gradient flow to GENERIC structure
Nonlinear Vlasov-Fokker-Planck dynamics admit a GENERIC structure that reduces to a generalized Wasserstein gradient flow whose trajectorial dissipation captures the nonlinear interaction and whose partial degeneracy produces a metric decomposition supporting a partial HWI inequality.