Related papers: Reflected generalized backward doubly SDEs driven …
In [5] the authors obtained Mean-Field backward stochastic differential equations (BSDE) associated with a Mean-field stochastic differential equation (SDE) in a natural way as limit of some highly dimensional system of forward and backward…
It was recently proven that the correlation function of the stationary version of a reflected L\'evy process is nonnegative, nonincreasing and convex. In another branch of the literature it was established that the mean value of the…
This paper presents existence and uniqueness results for reflected system of quasilinear stochastic partial differential equations in a convex domain D from Rk. The method is based on the probabilistic interpretation of the solution by…
In this paper, we study a class of reflected backward stochastic differential equations (BSDEs) of mean-field type, where the mean-field interaction in terms of the distribution of the $Y$-component of the solution enters in both the driver…
In this paper, we study reflected backward stochastic difference equations (RBSDEs for short) with finitely many states in discrete time. The general existence and uniqueness result, as well as comparison theorems for the solutions, are…
In this paper, we deal with a class of one-dimensional reflected backward stochastic differential equations with stochastic Lipschitz coefficient. We derive the existence and uniqueness of the solutions for those equations via Snell…
We establish existence and uniqueness for a wide class of Markovian systems of backward stochastic differential equations (BSDE) with quadratic nonlinearities. This class is characterized by an abstract structural assumption on the…
We study generalized backward stochastic differential equations (BSDEs) up to a random time horizon $\vartheta$, which is not a stopping time, under minimal assumptions regarding the properties of $\vartheta$. In contrast to existing works…
Mean-field backward doubly stochastic differential equations (MF-BDSDEs, for short) are introduced and studied. The existence and uniqueness of solutions for MF-BDSDEs is established. One probabilistic interpretation for the solutions to a…
We focus on a class of BSDEs driven by a cadlag martingale and corresponding Markov type BSDE which arise when the randomness of the driver appears through a Markov process. To those BSDEs we associate a deterministic problem which, when…
In this paper, we introduce a new kind of "variant" reflected backward doubly stochastic differential equations (VRBDSDEs in short), where the drift is the nonlinear function of the barrier process. In the one stochastic case, this type of…
Coupling by reflection mixed with synchronous coupling is constructed for a class of stochastic differential equations (SDEs) driven by L\'{e}vy noises. As an application, we establish the exponential contractivity of the associated…
The large deviations principles are established for a class of multidimensional degenerate stochastic differential equations with reflecting boundary conditions. The results include two cases where the initial conditions are adapted and…
Generalized B\"acklund-Darboux transformations (GBDTs) of discrete skew-selfadjoint Dirac systems have been successfully used for explicit solving of direct and inverse problems of Weyl-Titchmarsh theory. During explicit solving of the…
Large classes of multi-dimensional Gaussian processes can be enhanced with stochastic Levy area(s). In a previous paper, we gave sufficient and essentially necessary conditions, only involving variational properties of the covariance.…
We consider the problem of viscosity solution of integro-partial differential equation(IPDE in short) with one obstacle via the solution of reflected backward stochastic differential equations(RBSDE in short) with jumps. We show existence…
We present a unified approach to $L^p$-solutions ($p > 1$) of multidimensional backward stochastic differential equations (BSDEs) driven by L\'evy processes and more general filtrations. New existence, uniqueness and comparison results are…
In this paper, we study the well-posedness of multi-dimensional backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs) with diagonal generators, the $z$ parts of whose $l$-th components only depend on the…
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…
In this paper, we study backward doubly stochastic integral equations of the Volterra type (BDSIEVs in short). Under uniform Lipschitz assumptions, we establish an existence and uniqueness result.