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Jiagang Ren

Publications and source records attributed to Jiagang Ren.

12 recordsLinked to original sources
arXiv2026

Integration by Parts Formulas of Mckean-Vlasov SDEs with Jumps and Some Applications

In this article, we establish integration by parts formulas for the solutions of McKean-Vlasov stochastic differential equations with jumps under elliptic coefficients. The derived formulas accommodate both derivatives with respect to real-valued variables and measure-valued variables, interpreted through the Lions' derivative. As applications, we obtain estimates for the derivatives of the density functions of the McKean-Vlasov SDEs, and relying on the integration by parts formulas, we subsequently prove the existence and uniqueness of classical solutions to the associated PDEs with irregular terminal conditions.

math.PR↗
arXiv2025

Bismut-Elworthy-Li Formulae for Forward-Backward SDEs with Jumps and Applications

Under nondegeneracy assumptions on the diffusion coefficients, we establish the derivative formulae of Bismut-Elworthy-Li's type for forward-backward stochastic differential equations with respect to Poisson random measure using the lent particle method created by Bouleau and Denis, which is not given before. Applying this formula, the existence and uniqueness of a solution of nonlocal quasi-linear integral partial differential equations, which are differentiable with respect to the space variable, are obtained, even if the initial datum and coefficients of this equation are not.

math.PR↗
arXiv2016

On approximate continuity and the support of reflected stochastic differential equations

In this paper we prove an approximate continuity result for stochastic differential equations with normal reflections in domains satisfying Saisho's conditions, which together with the Wong-Zakai approximation result completes the support theorem for such diffusions in the uniform convergence topology. Also by adapting Millet and Sanz-Solé's idea, we characterize in Hölder norm the support of diffusions reflected in domains satisfying the Lions-Sznitman conditions by proving limit theorems of adapted interpolations. Finally we apply the support theorem to establish a boundary-interior maximum principle for subharmonic functions.

math.PR↗
arXiv2016

Penalization of Reflected SDEs and Neumann Problems of HJB Equations

In this paper we first study the penalization approximation of stochastic differential equations reflected in a domain which satisfies conditions (A) and (B) and prove that the sequence of solutions of the penalizing equations converges in the uniform topology to the solution of the corresponding reflected stochastic differential equation. Then by using this convergence result, we consider partial differential equations with Neumann boundary conditions in domains neither smooth nor convex and prove the existence and comparison principle of viscosity solutions of such nonlinear PDEs. Also, by applying the support of reflected diffusions established in \cite{ren-wuAP}, we establish the maximum principle for the viscosity solutions of linear PDEs with Neumann boundary conditions.

math.PR↗
arXiv2014

Localization of Wiener Functionals of Fractional Regularity and Applications

In this paper we localize some of Watanabe's results on fractional Wiener functionals, and use them to give a precise estimate of the difference between two Donsker's delta functionals even with fractional differentiability. As an application, the convergence rate of the density of the Euler scheme for non-Markovian stochastic differential equations is obtained.

math.PR↗
arXiv2008

Freidlin-Wentzell's Large Deviations for Stochastic Evolution Equations

We prove a Freidlin-Wentzell large deviation principle for general stochastic evolution equations with small perturbation multiplicative noises. In particular, our general result can be used to deal with a large class of quasi linear stochastic partial differential equations, such as stochastic porous medium equations and stochastic reaction diffusion equations with polynomial growth zero order term and $p$-Laplacian second order term.

math.PR↗
arXiv2006

Stochastic Generalized Porous Media and Fast Diffusion Equations

We present a generalization of Krylov-Rozovskii's result on the existence and uniqueness of solutions to monotone stochastic differential equations. As an application, the stochastic generalized porous media and fast diffusion equations are studied for $σ$-finite reference measures, where the drift term is given by a negative definite operator acting on a time-dependent function, which belongs to a large class of functions comparable with the so-called $N$-functions in the theory of Orlicz spaces.

math.PR↗