Related papers: Exponential Ergodicity for Singular Reflecting McK…

This work concerns a type of coupled McKean-Vlasov stochastic differential equations (MVSDEs in short) with jumps. First, we prove superposition principles for these coupled MVSDEs with jumps and non-local space-distribution dependent…

In this paper we explore the merit of relative entropy in proving weak well-posedness of McKean-Vlasov SDEs and SPDEs, extending the technique introduced in Lacker arxiv:2105.02983. In the SDE setting, we prove weak existence and uniqueness…

By using coupling by change of conditional probability measure, the log-Harnack inequality for path dependent McKean-Vlasov SDEs with distribution dependent diffusion coefficients is established, which together with the exponential…

In this paper we mainly investigate the strong and weak well-posedness of a class of McKean-Vlasov stochastic (partial) differential equations. The main existence and uniqueness results state that we only need to impose some local…

Recently Krylov established weak existence of solutions to SDEs for integrable drifts in mixed Lebesgue spaces, whose exponents satisfy the condition $1/q+d/p\leq 1$, thus going below the celebrated Ladyzhenskaya-Prodi-Serrin condition. We…

We consider a one-dimensional Stochastic Differential Equation with reflection where we allow the drift to be merely bounded and measurable. It is already known that such equations have a unique strong solution. Recently, it has been shown…

The classical result by It\^o on the existence of strong solutions of stochastic differential equations (SDEs) with Lipschitz coefficients can be extended to the case where the drift is only measurable and bounded. These generalizations are…

The time-evolution of a moderately dense gas in a vacuum is described in classical mechanics by a particle density function obtained from the Enskog equation. Based on a McKean-Vlasov stochastic equation with jumps, the associated…

We develop a general framework for studying ergodicity of order-preserving Markov semigroups. We establish natural and in a certain sense optimal conditions for existence and uniqueness of the invariant measure and exponential convergence…

This work focuses on a class of regime-switching neutral stochastic functional differential equations (RNSFDEs) with infinite delay, in which the switching component can possess finite or countably infinite many states. To ensure 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…

Inspired by the stochastic particle method, this paper establishes an easily implementable explicit numerical method for McKean-Vlasov stochastic differential equations (MV-SDEs) with superlinear growth coefficients. The paper establishes…

We consider multidimensional SDEs with singular drift $b$ and Sobolev diffusion coefficients $\sigma$, satisfying Krylov--R\"ockner type assumptions. We prove several stability estimates, comparing solutions driven by different…

We consider SDEs driven by multiplicative pure jump L\'{e}vy noises, where L\'evy processes are not necessarily comparable to $\alpha$-stable-like processes. By assuming that the SDE has a unique solution, we obtain gradient estimates of…

We study a class of ergodic BSDEs related to PDEs with Neumann boundary conditions. The randomness of the drift is given by a forward process under weakly dissipative assumptions with an invertible and bounded diffusion matrix. Furthermore,…

The log-Harnack inequality and Bismut formula are established for McKean-Vlasov SDEs with singularities in all (time, space, distribution) variables, where the drift satisfies an integrability condition in time-space, and the continuity in…

In this paper, concerning SDEs with H\"older continuous drifts, which are merely dissipative at infinity, and SDEs with piecewise continuous drifts, we investigate the strong law of large numbers and the central limit theorem for underlying…

This paper studies McKean-Vlasov stochastic differential equations (MVSDEs) whose drift coefficients grow super-linearly in both state variables and measure arguments, and whose diffusion coefficients exhibit super-linear growth in the…

In this article, exponential contraction in Wasserstein distance for heat semigroups of diffusion processes on Riemannian manifolds is established under curvature conditions where Ricci curvature is not necessarily required to be…

We study stochastic differential equations (SDEs) with multiplicative Stratonovich-type noise of the form $ dX_t = b(X_t) dt + \sigma(X_t)\circ d W_t, X_0=x_0\in\mathbb{R}^d, t\geq0,$ with a possibly singular drift $b\in…