Related papers: Invariant cones for jump-diffusions in infinite di…
The goal of this paper is to clarify when a closed convex cone is invariant for a stochastic partial differential equation (SPDE) driven by a Wiener process and a Poisson random measure, and to provide conditions on the parameters of the…
We establish necessary and sufficient conditions for stochastic invariance of closed subsets in Hilbert spaces for solutions to infinite-dimensional stochastic differential equations (SDEs) under mild assumptions on the coefficients. Our…
We provide necessary and sufficient first order geometric conditions for the stochastic invariance of a closed subset of R^d with respect to a jump-diffusion under weak regularity assumptions on the coefficients. Our main result extends the…
We provide necessary and sufficient conditions for stochastic invariance of finite dimensional submanifolds for solutions of stochastic partial differential equations (SPDEs) in continuously embedded Hilbert spaces with non-smooth…
In this note we provide conditions for local invariance of finite dimensional submanifolds for solutions to stochastic partial differential equations (SPDEs) in the framework of the variational approach. For this purpose, we provide a…
A series of recent articles introduced a method to construct stochastic partial differential equations (SPDEs) which are invariant with respect to the distribution of a given conditioned diffusion. These works are restricted to the case of…
In this paper, we investigate stochastic continuity (with respect to the initial value), irreducibility and non confluence property of the solutions of stochastic differential equations with jumps. The conditions we posed are weaker than…
We provide necessary and sufficient conditions for stochastic invariance of finite dimensional submanifolds with boundary in Hilbert spaces for stochastic partial differential equations driven by Wiener processes and Poisson random…
In this article we study (possibly degenerate) stochastic differential equations (SDE) with irregular (or discontiuous) coefficients, and prove that under certain conditions on the coefficients, there exists a unique almost everywhere…
This paper studies open-loop equilibriums for a general class of time-inconsistent stochastic control problems under jump-diffusion SDEs with deterministic coefficients. Inspired by the idea of Four-Step-Scheme for forward-backward…
We formulate a new class of stochastic partial differential equations (SPDEs), named high-order vector backward SPDEs (B-SPDEs) with jumps, which allow the high-order integral-partial differential operators into both drift and diffusion…
In the paper, we consider the no-explosion condition and pathwise uniqueness for SDEs driven by a Poisson random measure with coefficients that are super-linear and non-Lipschitz. We give a comparison theorem in the one-dimensional case…
In this paper we study jump-diffusion stochastic differential equations (SDEs) with a discontinuous drift coefficient and a possibly degenerate diffusion coefficient. Such SDEs appear in applications such as optimal control problems in…
In this paper, we study a very general stochastic variational inequality(SVI) having jumps, random coefficients, delay, and path dependence, in infinite dimensions. Well-posedness in terms of the existence and uniqueness of a solution is…
We study diffusion processes corresponding to infinite dimensional semilinear stochastic differential equations with local Lipschitz drift term and an arbitrary Lipschitz diffusion coefficient. We prove tightness and the Feller property of…
In this paper we obtain a comparison theorem for backward stochastic partial differential equation (SPDEs) with jumps. We apply it to introduce space-dependent convex risk measures as a model for risk in large systems of interacting…
We investigate which jump-diffusion models are convexity preserving. The study of convexity preserving models is motivated by monotonicity results for such models in the volatility and in the jump parameters. We give a necessary condition…
The classical result by It\^o on the existence of strong solutions of stochastic differential equations (SDEs) with Lipschitz coefficients can be extended to the case where the drift is only measurable and bounded. These generalizations are…
In this paper, we mainly focus on the set-valued (stochastic) analysis on the space of convex, closed, but possibly unbounded sets, and try to establish a useful theoretical framework for studying the set-valued stochastic differential…
Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…