Bismut formula for Lions derivative of distribution dependent SDEs and applications

DOI10.1016/j.jde.2019.05.016zbMath1415.60094arXiv1809.06068OpenAlexW2963302533MaRDI QIDQ2314013

Panpan Ren, Fengyu Wang

Publication date: 25 July 2019

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.06068

zbMATH Keywords

Bismut formulaWasserstein distancedistribution dependent SDEs\(L\)-derivative

Mathematics Subject Classification ID

Diffusion processes (60J60) Diffusion processes and stochastic analysis on manifolds (58J65)

Related Items (30)

Averaging principle for distribution dependent stochastic differential equations driven by fractional Brownian motion and standard Brownian motion ⋮ Linearization of nonlinear Fokker-Planck equations and applications ⋮ Distribution-dependent stochastic porous media equations ⋮ Regularity for distribution-dependent SDEs driven by jump processes ⋮ Least squares estimation for distribution-dependent stochastic differential delay equations ⋮ Distribution dependent SDEs driven by fractional Brownian motions ⋮ Bismut formula for intrinsic/Lions derivatives of distribution dependent SDEs with singular coefficients ⋮ Bismut formula for Lions derivative of distribution-path dependent SDEs ⋮ The averaging method for doubly perturbed distribution dependent SDEs ⋮ Asymptotic Bismut formulae for stochastic functional differential equations with infinite delay ⋮ Small noise asymptotics of multi-scale McKean-Vlasov stochastic dynamical systems ⋮ Asymptotic behaviors for distribution dependent SDEs driven by fractional Brownian motions ⋮ Stochastic control problem for distribution dependent SDE driven by a Gauss Volterra process ⋮ Large deviation principle for distribution dependent S(P)DEs with singular drift ⋮ Asymptotic behaviors of small perturbation for multivalued Mckean-Vlasov stochastic differential equations ⋮ On a class of distribution dependent stochastic differential equations driven by time-changed Brownian motions ⋮ An explicit Euler-Maruyama method for McKean-Vlasov SDEs driven by fractional Brownian motion ⋮ Derivative formula for singular McKean-Vlasov SDEs ⋮ Derivative formulas in measure on Riemannian manifolds ⋮ Well-posedness and averaging principle of McKean-Vlasov SPDEs driven by cylindrical α-stable process ⋮ Backpropagation in hyperbolic chaos via adjoint shadowing ⋮ Reflecting image-dependent SDEs in Wasserstein space and large deviation principle ⋮ Distribution-dependent SDEs with Hölder continuous drift and \(\alpha\)-stable noise ⋮ Strong averaging principle for two-time-scale stochastic McKean-Vlasov equations ⋮ Large deviation principle for McKean-Vlasov quasilinear stochastic evolution equations ⋮ Density functions of distribution dependent SDEs driven by Lévy noises ⋮ Strong convergence order for slow-fast McKean-Vlasov stochastic differential equations ⋮ Derivative estimates on distributions of McKean-Vlasov SDEs ⋮ Distribution dependent stochastic differential equations ⋮ Central limit theorem and moderate deviation principle for McKean-Vlasov SDEs

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