Author
Jinlong Wei
Bio: Jinlong Wei is an academic researcher from Zhongnan University of Economics and Law. The author has contributed to research in topics: Parabolic partial differential equation & Uniqueness. The author has an hindex of 4, co-authored 46 publications receiving 80 citations.
Papers
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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 ¯.
14 citations
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.
Abstract: In this paper, we study the fractional Fokker-Planck equation and obtain the existence and uniqueness of weak Lp-solutions (1 ⩽ p ⩽ ∞) under the assumptions that the coefficients are only in Sobolev spaces. Moreover, to L∞-solutions, we gain the well-posedness for BV coefficients. Besides, the non-negative weak Lp-solutions and renormalized solutions are derived. After then, we achieve the stability for stationary solutions.
13 citations
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.
Abstract: The aim of this paper is to establish the averaging principle for stochastic differential equations under a general averaging condition, which is weaker than the traditional case. Under this condition, we establish an effective approximation for the solution of stochastic differential equations in mean square.
9 citations
Journal Article•
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.
Abstract: We extend Krylov and Rockner's result \cite{KR} to the drift coefficients in critical Lebesgue space, and prove the existence and uniqueness of weak solutions for a class of SDEs. To be more precise, let $b: [0,T]\times{\mathbb R}^d\rightarrow{\mathbb R}^d$ be Borel measurable, where $T>0$ is arbitrarily fixed. Consider $$X_t=x+\int_0^tb(s,X_s)ds+W_t,\quad t\in[0,T], \, x\in{\mathbb R}^d,$$ where $\{W_t\}_{t\in[0,T]}$ is a $d$-dimensional standard Wiener process. If $b=b_1+b_2$ such that $b_1(T-\cdot)\in\mathcal{C}_q^0((0,T];L^p({\mathbb R}^d))$ with $2/q+d/p=1$ for $p,q\ge1$ and $\|b_1(T-\cdot)\|_{\mathcal{C}_q((0,T];L^p({\mathbb R}^d))}$ is sufficiently small, and that $b_2$ is bounded and Borel measurable, then there exits a unique weak solution to the above equation. Furthermore, we obtain the strong Feller property of the semi-group and existence of density associated with above SDE. Besides, we extend the classical partial differential equations (PDEs) results for $L^q(0,T;L^p({\mathbb R}^d))$ coefficients to $L^\infty_q(0,T;L^p({\mathbb R}^d))$ ones, and derive the Lipschitz regularity for solutions of second order parabolic PDEs (see Lemma 2.1).
8 citations
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...
Abstract: The goal of this paper is to establish the Lipschitz and W2,∞ estimates for a 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...
8 citations
Cited by
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01 Jan 1998
TL;DR: In this paper, the authors explore questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties, using diffusion processes as a model of a Markov process with continuous sample paths.
Abstract: We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.
2,446 citations
Book•
01 Jan 2013
TL;DR: In this paper, the authors consider the distributional properties of Levy processes and propose a potential theory for Levy processes, which is based on the Wiener-Hopf factorization.
Abstract: Preface to the revised edition Remarks on notation 1. Basic examples 2. Characterization and existence 3. Stable processes and their extensions 4. The Levy-Ito decomposition of sample functions 5. Distributional properties of Levy processes 6. Subordination and density transformation 7. Recurrence and transience 8. Potential theory for Levy processes 9. Wiener-Hopf factorizations 10. More distributional properties Supplement Solutions to exercises References and author index Subject index.
1,957 citations
01 Jan 2016
TL;DR: The stochastic differential equations and applications is universally compatible with any devices to read, and an online access to it is set as public so you can get it instantly.
Abstract: stochastic differential equations and applications is available in our digital library an online access to it is set as public so you can get it instantly. Our books collection saves in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the stochastic differential equations and applications is universally compatible with any devices to read.
741 citations