Jinlong Wei

TL;DR: In this article, the authors derived the BMO estimates and Morrey-Campanato estimates, respectively, for stochastic singular integral operators arising from the equations concerned, by utilizing the embedding theory between the Campanato space and the Holder space, and established the controllability of the norm of the space C θ, θ / 2 ( D ¯ ), where θ ≥ 0, D ¯ = [ 0, T ] × G ¯.

TL;DR: In this article, the existence and uniqueness of weak Lp-solutions under the assumption that the coefficients are only in Sobolev spaces is established. And the non-negative weak lp-Solutions and renormalized solutions are derived.

TL;DR: In this paper, the authors established the averaging principle for stochastic differential equations under a general averaging condition, which is weaker than the traditional case, and established an effective approximation for the solution of stochastically differential equations in mean square.

TL;DR: In this paper, the existence and uniqueness of weak solutions for a class of SDEs were proved for the drift coefficients in critical Lebesgue space, and the strong Feller property of the semi-group and existence of density associated with the above SDE was obtained.

TL;DR: In this article, the Lipschitz and W2 estimates for second-order parabolic PDE ∂tu(t,x) = 12Δu( t,x)+f(t,x) on Rd with zero initial data and f satisfying a Ladyzhenskaya-Prod...