Related papers: Backward Doubly Stochastic Equations with Jumps an…

This paper is concerned with a class of uncertain backward stochastic differential equations (UBSDEs) driven by both an $m$-dimensional Brownian motion and a $d$-dimensional canonical process with uniform Lipschitzian coefficients. Such…

In this paper we study the strong convergence for the Euler-Maruyama approximation of a class of stochastic differential equations whose both drift and diffusion coefficients are possibly discontinuous.

Quantum stochastic master equations of jump type are formulated in a general way and connections with quantum/classical hybrid systems and quantum filtering theory are discussed. By introducing the notion of ``typical trajectory", we show…

We extend some methods developed by Albeverio, Brze\'{z}niak and Wu and we show how to apply them in order to prove existence of global strong solutions of stochastic differential equations with jumps, under a local one-sided Lipschitz…

The Cauchy problem for a multidimensional linear transport equation with discontinuous coefficient is investigated. Provided the coefficient satisfies a one-sided Lipschitz condition, existence, uniqueness and weak stability of solutions…

In this paper the jump formulas for the double layer potential and other singular integrals are proved for arbitrary rectifiable sets, by defining suitable non-tangential limits. The arguments are quite straightforward and only require some…

In this paper we investigate classical solution of a semi-linear system of backward stochastic integral partial differential equations driven by a Brownian motion and a Poisson point process. By proving an It\^{o}-Wentzell formula for jump…

We prove an existence and uniqueness result for generalized backward doubly stochastic differential equations driven by L\'evy processes with non-Lipschitz assumptions.

For backward stochastic Volterra integral equations (BSVIEs) in multi-dimensional Euclidean spaces, comparison theorems are established in a systematic way for the adapted solutions and adapted M-solutions. For completeness, comparison…

In this paper, we study backward stochastic Volterra integral equations introduced in [26, 45] and extend the existence, uniqueness or comparison results for general filtration as in [31] (not only Brownian-Poisson setting). We also…

It is shown that some class of differential inclusions has solutions that are defined and bounded for all real values of independent variable. Applications to dynamics are considered.

We consider reflected backward stochastic differential equations with two general optional barriers. The solutions to these equations have the so-called regulated trajectories, i.e trajectories with left and right finite limits. We prove…

We explore Ito stochastic differential equations where the drift term possibly depends on the infinite past. Assuming the existence of a Lyapunov function, we prove the existence of a stationary solution assuming only minimal continuity of…

In this paper we consider one-dimensional diffusions with constant coefficients in a finite interval with jump boundary and a certain deterministic jump distribution. We use coupling methods in order to identify the spectral gap in the case…

Backward stochastic partial differential equations of parabolic type with variable coefficients are considered in smooth domains. Existence and uniqueness results are given in weighted Sobolev spaces allowing the derivatives of the…

We present a new version of the stochastic sewing lemma, capable of handling multiple discontinuous control functions. This is then used to develop a theory of rough stochastic analysis in a c\`adl\`ag setting. In particular, we define…

We consider boundary value problems for stochastic differential equations of second order with a small parameter. For this case we prove a special existence and unicity theorem for strong solutions. The asymptotic behavior of these…

We investigate the convergence of hitting times for jump-diffusion processes. Specifically, we study a sequence of stochastic differential equations with jumps. Under reasonable assumptions, we establish the convergence of solutions to the…

We survey and refine recent results on weak and strong well-posedness of stochastic differential equations with singular drift satisfying some minimal assumptions.

We prove that under natural assumptions on the data strong solutions in Sobolev spaces of semilinear parabolic equations in divergence form involving measure on the right-hand side may be represented by solutions of some generalized…