The distribution dependent stochastic differential equations (DDSDEs) describe stochastic
systems whose evolution is determined by both the microcosmic site and the macrocosmic …

The key point of Harnack's inequality is to compare values at two different points for positive
solutions of a partial differential equation. This inequality was introduced by Harnack [21] in …

To characterize the Neumann problem for nonlinear Fokker-Planck equations, we
investigate distribution dependent reflecting stochastic differential equations (DDRSDEs) in …

The stochastic convective Brinkman-Forchheimer (SCBF) equations or the tamed Navier-
Stokes equations in bounded or periodic domains are considered in this work. We show the …

We introduce a new framework of Markovian lifts of stochastic Volterra integral equations
(SVIEs for short) with completely monotone kernels. We define the state space of the …

We formulate a new information-theoretic principle—the shifted composition rule—which
bounds the divergence (eg, Kullback-Leibler or Rényi) between the laws of two stochastic …

In this paper we prove a derivative formula of Bismut–Elworthy–Li's type as well as a
gradient estimate for stochastic differential equations driven by α-stable noises, where α∈(0 …

By constructing successful couplings for degenerate diffusion processes, explicit derivative
formula and Harnack type inequalities are presented for solutions to a class of degenerate …

Let (M, ρ) be a connected compact Riemannian manifold without boundary or with a convex
boundary∂ M, let V∈ C 2 (M) such that μ (dx):= e V (x) dx is a probability measure, where …

We obtain two elliptic gradient estimates for positive solutions to the f f-heat equation on a
complete smooth metric measure space with only Bakry–Émery Ricci tensor bounded …