相关论文: Derivative Formula and Harnack Inequality for Dege…

The distribution-dependent stochastic differential equations (DDSDEs) describe stochastic systems whose evolution is determined by both the microcosmic site and the macrocosmic distribution of the particle. The density function associated…

The purpose of this paper is to investigate the existence of the Onsager-Machlup action functional for degenerate McKean-Vlasov stochastic differential equations. To this end, we first derive Onsager-Machlup action functional for degenerate…

Explicit sufficient conditions on the hypercontractivity are presented for two classes of functional stochastic partial differential equations driven by, respectively, non-degenerate and degenerate Gaussian noises. Consequently, these…

Under integrability conditions on distribution dependent coefficients, existence and uniqueness are proved for McKean-Vlasov type SDEs with non-degenerate noise. When the coefficients are Dini continuous in the space variable, gradient…

We establish Harnack inequalities for viscosity solutions of a class of degenerate fully nonlinear anisotropic elliptic equations exhibiting non-standard growth conditions. A primary example of such operators is the degenerate anisotropic…

In this paper, the coupling by change of measure is constructed for a class of SDEs with integrable drift and additive noise, from which the Harnack and shift Harnack inequalities are derived. Finally, as applications, the gradient…

Existence and uniqueness results of fully coupled forward stochastic differential equations without drifts and backward stochastic differential equations in a degenerate case are obtained for an arbitrarily large time duration.

In this paper, we present a unified method for deriving differential Harnack inequalities for positive solutions of the semilinear parabolic equation \begin{equation*} \partial_t u=\Delta_V u+H(u) \end{equation*} on complete Riemannian…

When studying boundary value problems for some partial differential equations arising in applied mathematics, we often have to study the solution of a system of partial differential equations satisfied by hypergeometric functions and find…

For a general class of divergence type quasi-linear degenerate parabolic equations with measurable coeffcients and lower order terms from non-linear Kato-type classes, we prove local boundedness and continuity of solutions, and the…

We obtain an analytic proof for asymptotic H\"older estimate and Harnack's inequality for solutions to a discrete dynamic programming equation. The results also generalize to functions satisfying Pucci-type inequalities for discrete…

In the present article, solvability in Sobolev spaces is investigated for a class of degenerate stochastic integro-differential equations of parabolic type. Existence and uniqueness is obtained, and estimates are given for the solution.

By using coupling argument and regularization approximations of the underlying subordinator, dimension-free Harnack inequalities are established for a class of stochastic equations driven by a L\'evy noise containing a subordinate Brownian…

Situations of a functional predictor paired with a scalar response are increasingly encountered in data analysis. Predictors are often appropriately modeled as square integrable smooth random functions. Imposing minimal assumptions on the…

We study stochastic differential equations with jumps with no diffusion part. We provide some basic stochastic characterizations of solutions of the corresponding non-local partial differential equations and prove the Harnack inequality for…

Systems of parabolic, possibly degenerate parabolic SPDEs are considered. Existence and uniqueness are established in Sobolev spaces. Similar results are obtained for a class of equations generalizing the deterministic first order symmetric…

By using the Malliavin calculus and finite jump approximations, the Driver-type integration by parts formula is established for the semigroup associated to stochastic (partial) differential equations with noises containing a subordinate…

We study some functional inequalities satisfied by the distribution of the solution of a stochastic differential equation driven by fractional Brownian motions. Such functional inequalities are obtained through new integration by parts…

We prove an invariant Harnack's inequality for operators in non-divergence form structured on Heisenberg vector fields when the coefficient matrix is uniformly positive definite, continuous, and symplectic. The method consists in…

In the paper, we are concerned with degenerate stochastic differential equations with jumps. Firstly, we establish two support theorems for the solutions of the degenerate stochastic equations, under different (sufficient) conditions.…