Related papers: Backward stochastic variational inequalities on ra…
We study linear stochastic partial differential equations of parabolic type. We consider a new boundary value problem where a Cauchy condition is replaced by a prescribed average of the solution either over time and probabilistic space for…
This paper is devoted to solving a multidimensional backward stochastic differential equation with a general time interval, where the generator is uniformly continuous in $(y,z)$ non-uniformly with respect to $t$. By establishing some…
This paper is an attempt to extend the notion of viscosity solution to nonlinear stochastic partial differential integral equations with nonlinear Neumann boundary condition. Using the recently developed theory on generalized backward…
We study the existence and uniqueness of the solution for the following backward stochastic variational inequality with oblique reflection (for short, $BSVI\left(H(t,y),\varphi,F\right)$), written under differential form \[…
We prove existence and uniqueness for a one-dimensional multivalued backward stochastic differential equation with jumps. The equation involves a time-indexed family of maximal monotone operators $k_t(\cdot)$ associated with increasing…
The work concerns a type of backward multivalued McKean-Vlasov stochastic differential equations. First, we prove the existence and uniqueness of solutions for backward multivalued McKean-Vlasov stochastic differential equations. Then, it…
The objective of this work is to prove, in a first step, the existence and the uniqueness of a solution of the following multivalued deterministic differential equation: $dx(t)+\partial ^-\varphi (x(t))(dt)\ni dm(t),\ t>0$, $x(0)=x_0$,…
The aim of this article is to study the asymptotic behaviour for large times of solutions to a certain class of stochastic partial differential equations of parabolic type. In particular, we will prove the backward uniqueness result and the…
By analogy with the theory of Backward Stochastic Differential Equations, we define Backward Stochastic Difference Equations on spaces related to discrete time, finite state processes. This paper considers these processes as constructions…
Backward stochastic partial differential equations of parabolic type in bounded domains are studied in the setting where the coercivity condition is not necessary satisfied and the equation can be degenerate. Some generalized solutions…
This paper is concerned with the strong solution to the Cauchy-Dirichlet problem for backward stochastic partial differential equations of parabolic type. Existence and uniqueness theorems are obtained, due to an application of the…
In this paper, we deal with a class of multivalued backward doubly stochastic differential equations with time delayed coefficients. Based on a slight extension of the existence and uniqueness of solutions for backward doubly stochastic…
In this paper we study a class of backward stochastic differential equations (BSDEs) of the form dY(t)= -AY(t)dt -f_0(t,Y(t))dt -f_1(t,Y(t),Z(t))dt + Z(t)dW(t) on the interval [0,T], with given final condition at time T, in an infinite…
In this paper, we deal with one dimensional backward doubly stochastic differential equations (BDSDEs) where the coefficient is left Lipschitz in y (may be discontinuous) and uniformly continuous in z. We obtain a generalized comparison…
Backward stochastic partial differential equations of parabolic type with variable coefficients are considered in the whole Euclidean space. Improved existence and uniqueness results are given in the Sobolev space $H^n$ ($=W^n_2$) under…
Bougerol (1993) and Straumann and Mikosch (2006) gave conditions under which there exists a unique stationary and ergodic solution to the stochastic difference equation $Y_t \overset{a.s.}{=} \Phi_t (Y_{t-1}), t \in \mathbb{Z}$ where…
This paper is concerned with the quasi-linear reflected backward stochastic partial differential equation (RBSPDE for short). Basing on the theory of backward stochastic partial differential equation and the parabolic capacity and…
In this paper, we study a multidimensional backward stochastic differential equation (BSDE) with an additional rough drift (rough BSDE), and give the existence and uniqueness of the adapted solution, either when the terminal value and the…
We address a class of backward stochastic differential equations on a bounded interval, where the driving noise is a marked, or multivariate, point process. Assuming that the jump times are totally inaccessible and a technical condition…
This course is intended as an introduction to the analysis of elliptic partial differential equations. The objective is to provide a large overview of the different aspects of elliptic partial differential equations and their modern…