Related papers: Density estimates for sdes driven by tempered stab…

We consider a Stochastic Differential Equation driven by a L\'evy process whose L\'evy measure satisfy a tempered stable domination. We study how a perturbation of the coefficients reflects on the density of the solution. We quantify the…

We consider a stable driven degenerate stochastic differential equation, whose coefficients satisfy a kind of weak H{\"o}rmander condition. Under mild smoothness assumptions we prove the uniqueness of the martingale problem for the…

In this article we show that a finite dimensional stochastic differential equation driven by a L\'evy process can be formulated as a stochastic partial differential equation. We prove the existence and uniqueness of strong solutions of such…

We investigate exponential stock models driven by tempered stable processes, which constitute a rich family of purely discontinuous L\'{e}vy processes. With a view of option pricing, we provide a systematic analysis of the existence of…

We consider the formal SDE dX t = b(t, X t)dt + dZ t , X 0 = x $\in$ R d , (E) where b $\in$ L r ([0, T ], B $\beta$ p,q (R d , R d)) is a time-inhomogeneous Besov drift and Z t is a symmetric d-dimensional $\alpha$-stable process, $\alpha$…

We study stochastic heat equations driven by a class of L\'evy processes: du = \De u dt + g dX_t \quad in \quad \bR^d_T, \qquad u(0,x)= 0 \quad in \quad x \in \bR^d. We prove the corresponding estimate \[\norm{u}_{\bH_p^k(\RT)} \le c(p,T)…

In this work, by using the Malliavin calculus, under H\"ormander's condition, we prove the existence of distributional densities for the solutions of stochastic differential equations driven by degenerate subordinated Brownian motions.…

In this article we study the existence and uniqueness of strong solutions of a class of parameterized family of SDEs driven by L\'evy noise. These SDEs occurs in connection with a class of stochastic PDEs, which take values in the space of…

In this paper we develop an $L_2$-theory for stochastic partial differential equations driven by L\'evy processes. The coefficients of the equations are random functions depending on time and space variables, and no smoothness assumption of…

In this article we study a class of stochastic functional differential equations driven by L\'{e}vy processes (in particular, $\alpha$-stable processes), and obtain the existence and uniqueness of Markov solutions in small time intervals.…

In this article we develop a method for the strong approximation of stochastic differential equations (SDEs) driven by L\'evy processes or general semimartingales. The main ingredients of our method is the perturbation of the SDE and the…

In this paper, we deal with a class of backward doubly stochastic differential equations (BDSDEs, in short) involving subdifferential operator of a convex function and driven by Teugels martingales associated with a L\'evy process. We show…

Using heat kernel estimates, we prove the pathwise uniqueness for strong solutions of irregular stochastic differential equation driven by a family of Markov process, whose generator is a non-local and non-symmetric L\'evy type operator.…

A new class of generalized backward doubly stochastic differential equations (GBDSDEs in short) driven by Teugels martingales associated with L\'evy process are investigated. We establish a comparison theorem which allows us to derive an…

We establish heat-kernel bounds and regularity estimates for the transition densities of the diffusion associated with the martingale problem corresponding to the generator of a formal multidimensional Brownian SDE with singular drift. As a…

In this paper, a class of reflected generalized backward doubly stochastic differential equations (reflected GBDSDEs in short) driven by Teugels martingales associated with L\'{e}vy process and the integral with respect to an adapted…

In this paper, we deal with a class of reflected backward stochastic differential equations associated to the subdifferential operator of a lower semi-continuous convex function driven by Teugels martingales associated with L\'{e}vy…

In this paper, we investigate the well-posedness of the martingale problem associated to non-linear stochastic differential equations (SDEs) in the sense of McKean-Vlasov under mild assumptions on the coefficients as well as classical…

Based on a class of moderately interacting particle systems, we establish a quantitative approximation for density-dependent McKean-Vlasov SDEs and the corresponding nonlinear, nonlocal PDEs. The SDE is driven by both Brownian motion and…

Marcus stochastic differential equations (SDEs) often are appropriate models for stochastic dynamical systems driven by non-Gaussian Levy processes and have wide applications in engineering and physical sciences. The probability density of…