Strong solutions of mean-field stochastic differential equations with irregular drift

DOI10.1214/18-EJP259zbMath1406.60083arXiv1806.11451OpenAlexW2963416210MaRDI QIDQ1722032

Martin Bauer, Thilo Meyer-Brandis, Frank Norbert Proske

Publication date: 14 February 2019

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.11451

zbMATH Keywords

Malliavin calculusstrong solutionsmean-field stochastic differential equationMcKean-Vlasov equationBismut-Elworthy-Li formulairregular coefficientslocal-time integralSobolev differentiability in the initial condition

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Applications of stochastic analysis (to PDEs, etc.) (60H30) Stochastic calculus of variations and the Malliavin calculus (60H07) Stochastic integral equations (60H20)

Related Items (23)

Distribution dependent SDEs driven by additive continuous noise ⋮ On the stability of mean-field stochastic differential equations with irregular expectation functional ⋮ Approximations of McKean-Vlasov stochastic differential equations with irregular coefficients ⋮ A flexible split-step scheme for solving McKean-Vlasov stochastic differential equations ⋮ A MEAN-FIELD EXTENSION OF THE LIBOR MARKET MODEL ⋮ Singular McKean-Vlasov (reflecting) SDEs with distribution dependent noise ⋮ Quantitative particle approximation of nonlinear Fokker-Planck equations with singular kernel ⋮ Mean-field stochastic differential equations with a discontinuous diffusion coefficient ⋮ Distribution dependent SDEs driven by additive fractional Brownian motion ⋮ Path dependent McKean-Vlasov SDEs with Hölder continuous diffusion ⋮ Log-Harnack inequality and exponential ergodicity for distribution dependent Chan-Karolyi-Longstaff-Sanders and Vasicek models ⋮ Online parameter estimation for the McKean-Vlasov stochastic differential equation ⋮ Restoration of well-posedness of infinite-dimensional singular ODE's via noise ⋮ Large deviations for interacting particle systems: joint mean-field and small-noise limit ⋮ Strong solutions of mean-field stochastic differential equations with irregular drift ⋮ Distribution-dependent SDEs with Hölder continuous drift and \(\alpha\)-stable noise ⋮ An adaptive Euler-Maruyama scheme for Mckean-Vlasov SDEs with super-linear growth and application to the mean-field Fitzhugh-Nagumo model ⋮ McKean-Vlasov SDEs with drifts discontinuous under Wasserstein distance ⋮ Weak solutions to Vlasov–McKean equations under Lyapunov-type conditions ⋮ Approximation of solutions of mean-field stochastic differential equations ⋮ McKean-Vlasov type stochastic differential equations arising from the random vortex method ⋮ Well-posedness and tamed schemes for McKean-Vlasov equations with common noise ⋮ Well-posedness and numerical schemes for one-dimensional McKean-Vlasov equations and interacting particle systems with discontinuous drift

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