Related papers: Distribution Dependent SDEs with Singular Coeffici…
We show existence of an invariant probability measure for a class of functional McKean-Vlasov SDEs by applying Kakutani's fixed point theorem to a suitable class of probability measures on a space of continuous functions. Unlike some…
By constructing successful couplings, the derivative formula, gradient estimates and Harnack inequalities are established for the semigroup associated with a class of degenerate functional stochastic differential equations.
We propose a new type SDE depending on the future distributions with all initial values, and establish the correspondence between this equation and the associated singular nonlinear PDE. Well-posedness and regularities are investigated.
The exponential ergodicity of partially dissipative McKean-Vlasov SDEs in the \(L^1\)-Wasserstein distance has been extensively studied using asymptotic reflection coupling. However, the reflection coupling method is not applicable for the…
The purpose of this paper is to study some properties of solutions to one dimensional as well as multidimensional stochastic differential equations (SDEs in short) with super-linear growth conditions on the coefficients. Taking inspiration…
The existence-uniqueness and stability of strong solutions are proved for a class of degenerate stochastic differential equations, where the noise coeffcicient might be non-Lipschitz, and the drift is locally Dini continuous in the…
Retarded stochastic differential equations (SDEs) constitute a large collection of systems arising in various real-life applications. Most of the existing results make crucial use of dissipative conditions. Dealing with "pure delay" systems…
We establish an asymptotic log-Harnack inequality for stochastic differential equations on $\R^d$ whose coefficients depend on the path and distribution for the whole history, allowing the drift to contain a Dini continuous term. The result…
We establish strong well-posedness for a class of degenerate SDEs of kinetic type with autonomous diffusion driven by a symmetric $\alpha$-stable process under H\"older regularity conditions for the drift term. We partially recover the…
Consider the density dependent (i.e. Nemytskii-type) SDEs on $\mathbb R^d$, where the drift $b_t(x,\rho(x),\rho)$ is locally integrable in $(t,x)\in [0,\infty)\times \mathbb R^d$ and may be singular in the distribution density function…
We study McKean-Vlasov SDEs with interaction kernels in $\tt W^{-\dd,k},$ the local negative Sobolev space on $\R^d$ with indexes $\dd \in [0,\infty)$ and $k\in [1,\infty].$ We derive the local well-posedness for any singular indexes…
We consider stochastic partial differential equations under minimal assumptions: the coefficients are merely bounded and measurable and satisfy the stochastic parabolicity condition. In particular, the diffusion term is allowed to be…
By using the ultracontractivity of a reference diffusion semigroup, Krylov's estimate is established for a class of degenerate SDEs with singular drifts, which leads to existence and pathwise uniqueness by means of Zvonkin's transformation.…
The existence and uniqueness of mild solutions are proved for a class of degenerate stochastic differential equations on Hilbert spaces where the drift is Dini continuous in the component with noise and H\"older continuous of order larger…
We prove pathwise uniqueness for a class of stochastic differential equations (SDE) on a Hilbert space with cylindrical Wiener noise, whose nonlinear drift parts are sums of the sub-differential of a convex function and a bounded part. This…
By using a regularity approximation argument, the global existence and uniqueness are derived for a class of nonlinear SPDEs depending on both the whole history and the distribution under strong enough noise. As applications, the global…
In this paper, Wang's log-Harnack inequality and exponential ergodicity are derived for two types of distribution dependent SDEs: one is the CKLS model, where the diffusion coefficient is a power function of order $\theta$ with…
In this paper we show the existence and uniqueness for a class of density dependent SDEs with bounded measurable drift, where the existence part is based on Euler's approximation for density dependent SDEs and the uniqueness is based on the…
We present a criterion for uniform in time convergence of the weak error of the Euler scheme for Stochastic Differential equations (SDEs). The criterion requires i) exponential decay in time of the space-derivatives of the semigroup…
The couplings by change of measure are applied to establish log-Harnack inequality(equivalently the entropy-cost estimate) for conditional McKean-Vlasov SDEs and derive the quantitative conditional propagation of chaos in relative entropy…