Related papers: Invariance of closed convex cones for stochastic p…
In this paper we provide sufficient conditions for stochastic invariance of closed convex cones for stochastic partial differential equations (SPDEs) of jump-diffusion type, and clarify when these conditions are necessary. Our results apply…
We prove that Poisson measures are invariant under (random) intensity preserving transformations whose finite difference gradient satisfies a cyclic vanishing condition. The proof relies on moment identities of independent interest for…
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…
We provide existence and uniqueness of global (and local) mild solutions for a general class of semilinear stochastic partial differential equations driven by Wiener processes and Poisson random measures under local Lipschitz and linear…
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 paper parabolic random partial differential equations and parabolic stochastic partial differential equations driven by a Wiener process are considered. A deterministic, tensorized evolution equation for the second moment and the…
The aim of this paper is to explore the relationship between invariant cones and nonlinear normal modes in piecewise linear mechanical systems. As a key result, we extend the invariant cone concept, originally established for homogeneous…
This paper focuses on the invariant measure of McKean-Vlasov (MV) stochastic differential equations (SDEs) with common noise (wCN) whose coefficients depend on both the state and the measure. Using the existence of the unique solution of…
In this work, we investigate the McKean-Vlasov stochastic partial differential equations driven by Poisson random measure. By adapting the variational framework, we prove the well-posedness and large deviation principle for a class of…
This article is devoted to the analysis of semilinear, parabolic, Stochastic Partial Differential Equations, with slow and fast time scales. Asymptotically, an averaging principle holds: the slow component converges to the solution of…
The intrinsic volumes of a convex cone are geometric functionals that return basic structural information about the cone. Recent research has demonstrated that conic intrinsic volumes are valuable for understanding the behavior of random…
The convergence of stochastic integrals driven by a sequence of Wiener processes $W_n\to W$ (with convergence in $C_t$) is crucial in the analysis of stochastic partial differential equations (SPDEs). The convergence we focus on in this…
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…
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…
This paper provides a new characterization of the stochastic invariance of a closed subset of R^d with respect to a diffusion. We extend the well-known inward pointing Stratonovich drift condition to the case where the diffusion matrix can…
The aim of this paper is to investigate the existence of optimal controls for systems described by stochastic partial differential equations (SPDEs) with locally monotone coefficients controlled by different external forces which are…
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…
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…
Solutions of a variational inequality are found by giving conditions for the monotone convergence with respect to a cone of the Picard iteration corresponding to its natural map. One of these conditions is the isotonicity of the projection…
In this paper, we study a class of slow-fast stochastic partial differential equations with multiplicative Wiener noise. Under some appropriate conditions, we prove the slow component converges to the solution of the corresponding averaged…