Existence and uniqueness of martingale solutions for SDEs with rough or degenerate coefficients

From MaRDI portal

Publication:2469818

Jump to:navigation, search

DOI10.1016/j.jfa.2007.09.020zbMath1169.60010OpenAlexW2074565352WikidataQ112632387 ScholiaQ112632387MaRDI QIDQ2469818

Alessio Figalli

Publication date: 11 February 2008

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2007.09.020

zbMATH Keywords

Fokker-Planck equation stochastic differential equations martingale solutions degenerate coefficients

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Martingales with continuous parameter (60G44) Ordinary differential equations and systems with randomness (34F05)

Related Items

Nonlinear Fokker-Planck equation with reflecting boundary conditions ⋮ Linearization of nonlinear Fokker-Planck equations and applications ⋮ On the Wellposedness of Some McKean Models with Moderated or Singular Diffusion Coefficient ⋮ Nonlinear Fokker–Planck Equations with Time-Dependent Coefficients ⋮ Path-Based Divergence Rates and Lagrangian Uncertainty in Stochastic Flows ⋮ Stability estimates for invariant measures of diffusion processes, with applications to stability of moment measures and Stein kernels ⋮ Optimal control of stochastic differential equations via Fokker-Planck equations ⋮ Renormalization and energy conservation for axisymmetric fluid flows ⋮ On the Cauchy problem for Fokker-Planck-Kolmogorov equations with potential terms on arbitrary domains ⋮ Flow selections for (nonlinear) Fokker-Planck-Kolmogorov equations ⋮ On the Discretization of Some Nonlinear Fokker--Planck--Kolmogorov Equations and Applications ⋮ Probabilistic Representation for Solutions to Nonlinear Fokker--Planck Equations ⋮ Well-posedness of the transport equation by stochastic perturbation ⋮ Mean field limit and propagation of chaos for Vlasov systems with bounded forces ⋮ Strong solutions to stochastic differential equations with rough coefficients ⋮ Uniqueness and propagation of chaos for the Boltzmann equation with moderately soft potentials ⋮ Three superposition principles: currents, continuity equations and curves of measures ⋮ Uniqueness for solutions of Fokker-Planck equations related to singular SPDE driven by Lévy and cylindrical Wiener noise ⋮ Transport distances for PDEs: the coupling method ⋮ On the convergence of closed-loop Nash equilibria to the mean field game limit ⋮ On uniqueness of solutions to the Cauchy problem for degenerate Fokker-Planck-Kolmogorov equations ⋮ The Itô SDEs and Fokker–Planck equations with Osgood and Sobolev coefficients ⋮ Probabilistic and deterministic algorithms for space multidimensional irregular porous media equation ⋮ Optimal control of the Fokker-Planck equation with space-dependent controls ⋮ Propagation of chaos for rank-based interacting diffusions and long time behaviour of a scalar quasilinear parabolic equation ⋮ Stochastic continuity equation with nonsmooth velocity ⋮ Well posedness of ODE's and continuity equations with nonsmooth vector fields, and applications ⋮ \(L^p\)-solutions of Fokker-Planck equations ⋮ A restricted superposition principle for (non-)linear Fokker-Planck-Kolmogorov equations on Hilbert spaces ⋮ Error estimates for a finite volume scheme for advection–diffusion equations with rough coefficients ⋮ Existence and uniqueness of weak solutions to Ginzburg-Landau equation with external noise and stochastic perturbation ⋮ Stationary solutions and local equations for interacting diffusions on regular trees ⋮ Uniqueness in law for a class of degenerate diffusions with continuous covariance ⋮ Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients ⋮ Existence and uniqueness of solutions for Fokker-Planck equations on Hilbert spaces ⋮ Propagation of chaos for aggregation equations with no-flux boundary conditions and sharp sensing zones ⋮ Lecture notes on the DiPerna–Lions theory in abstract measure spaces ⋮ A Malliavin calculus method to study densities of additive functionals of SDE's with irregular drifts ⋮ Superposition principle for the Fokker-Planck-Kolmogorov equations with unbounded coefficients ⋮ Superposition principle for non-local Fokker-Planck-Kolmogorov operators ⋮ Alessio Figalli: magic, method, mission ⋮ Probabilistic representation for solutions of an irregular porous media type equation ⋮ A new Markov selection procedure for degenerate diffusions ⋮ Existence and Uniqueness of Solutions to Fokker–Planck Type Equations with Irregular Coefficients ⋮ Euler scheme for density dependent stochastic differential equations ⋮ Propagation of chaos for the 2D viscous vortex model ⋮ On the Markovian projection in the Brunick-Shreve mimicking result ⋮ Regularity of solutions to differential equations with non-Lipschitz coefficients ⋮ On the uniqueness of integrable and probability solutions to the Cauchy problem for the Fokker-Planck-Kolmogorov equations ⋮ Existence and uniqueness results for time-inhomogeneous time-change equations and Fokker-Planck equations ⋮ Generalized stochastic flows and applications to incompressible viscous fluids ⋮ Lagrangian Uncertainty Quantification and Information Inequalities for Stochastic Flows ⋮ On uniqueness problems related to the Fokker-Planck-Kolmogorov equation for measures ⋮ Quantitative stability estimates for Fokker-Planck equations ⋮ Weak uniqueness of Fokker-Planck equations with degenerate and bounded coefficients ⋮ Weak solutions to Fokker-Planck equations and mean field games ⋮ Stochastic flows of SDEs with irregular coefficients and stochastic transport equations ⋮ Stochastic differential equations with coefficients in Sobolev spaces ⋮ Existence of flows for linear Fokker-Planck-Kolmogorov equations and its connection to well-posedness ⋮ Infinite-dimensional polynomial processes ⋮ Stochastic optimal transport revisited ⋮ Absolute continuity under flows generated by SDE with measurable drift coefficients ⋮ On the Ambrosio-Figalli-Trevisan superposition principle for probability solutions to Fokker-Planck-Kolmogorov equations ⋮ On convergence to stationary distributions for solutions of nonlinear Fokker-Planck-Kolmogorov equations ⋮ Stochastic ODEs and stochastic linear PDEs with critical drift: regularity, duality and uniqueness ⋮ On the superposition principle for Fokker-Planck-Kolmogorov equations ⋮ Statistical Stability for Transport in Random Media ⋮ Stochastic Hamiltonian flows with singular coefficients ⋮ Semiclassical limit of quantum dynamics with rough potentials and well‐posedness of transport equations with measure initial data ⋮ On flows associated to Sobolev vector fields in Wiener spaces: An approach à la DiPerna-Lions ⋮ On weak uniqueness for some degenerate SDEs by global \(L^p\) estimates ⋮ Quantitative estimates of propagation of chaos for stochastic systems with \(W^{-1,\infty}\) kernels ⋮ Uniqueness problems for degenerate Fokker-Planck-Kolmogorov equations ⋮ Well-posedness of distribution dependent SDEs with singular drifts ⋮ Existence, Uniqueness, and Regularity Results for Elliptic Equations with Drift Terms in Critical Weak Spaces ⋮ A class of stochastic differential equations with pathwise unique solutions ⋮ Remarks on uniqueness and strong solutions to deterministic and stochastic differential equations ⋮ Lagrangian flows driven by \(BV\) fields in Wiener spaces ⋮ Quasi-invariance of Lebesgue measure under the homeomorphic flow generated by SDE with non-Lipschitz coefficient ⋮ Renormalized Solutions for Stochastic Transport Equations and the Regularization by Bilinear Multiplicative Noise ⋮ Fokker-Planck equations with terminal condition and related McKean probabilistic representation ⋮ Uniqueness for Solutions of Fokker–Planck Equations on Infinite Dimensional Spaces ⋮ From Bachelier to Dupire via optimal transport ⋮ On the equivalence between some jumping SDEs with rough coefficients and some non-local PDEs ⋮ Propagation of chaos for the Vlasov-Poisson-Fokker-Planck system in 1D ⋮ A Benamou-Brenier formulation of martingale optimal transport ⋮ Existence of periodic probability solutions to Fokker-Planck equations with applications ⋮ Schauder estimates for nonlocal kinetic equations and applications ⋮ Optimal control of diffusion processes with terminal constraint in law ⋮ From nonlinear Fokker-Planck equations to solutions of distribution dependent SDE ⋮ Support theorem for stochastic differential equations with Sobolev coefficients ⋮ The Controllability of Fokker--Planck Equations with Reflecting Boundary Conditions and Controllers in Diffusion Term ⋮ Hitting Times, Occupation Times, Trivariate Laws and the Forward Kolmogorov Equation for a One-Dimensional Diffusion with Memory ⋮ A note on stochastic semilinear equations and their associated Fokker-Planck equations ⋮ Optimal stability estimates and a new uniqueness result for advection-diffusion equations ⋮ Joint Modeling and Calibration of SPX and VIX by Optimal Transport ⋮ Fokker-Planck-Kolmogorov equations with a potential term on a domain ⋮ Mean field limit for the one dimensional Vlasov-Poisson~equation ⋮ A semi-Lagrangian scheme for a degenerate second order mean field game system ⋮ Calibration of local‐stochastic volatility models by optimal transport ⋮ Kolmogorov Problems on Equations for Stationary and Transition Probabilities of Diffusion Processes ⋮ Linearization and a superposition principle for deterministic and stochastic nonlinear Fokker-Planck-Kolmogorov equations ⋮ Non-equilibrium large deviations and parabolic-hyperbolic PDE with irregular drift ⋮ Sharp uniform-in-time propagation of chaos ⋮ Strong solutions to McKean-Vlasov SDEs with coefficients of Nemytskii-type ⋮ L1-Theory for Hele-Shaw flow with linear drift ⋮ Limit theorems of invariant measures for multivalued McKean-Vlasov stochastic differential equations ⋮ Weak and parabolic solutions of advection-diffusion equations with rough velocity field ⋮ Variability of paths and differential equations with \(\mathrm{BV}\)-coefficients ⋮ Controlling a generalized Fokker-Planck equation via inputs with nonlocal action ⋮ Stochastic Lagrangian perturbation of Lie transport and applications to fluids ⋮ Weak well-posedness for a class of degenerate Lévy-driven SDEs with Hölder continuous coefficients ⋮ Superposition and mimicking theorems for conditional McKean-Vlasov equations

Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:2469818&oldid=15161883"