The systematic study of existence, uniqueness, and properties of solutions to stochastic
differential equations in infinite dimensions arising from practical problems characterizes this …

The study of stochastic differential equations (SDEs) driven by Lévy processes in R
originated in the book by Skorokhod [97]. In view of the Lévy–Itô decomposition, he reduced …

Existence and uniqueness of the mild solutions for stochastic differential equations for
Hilbert valued stochastic processes are discussed, with the multiplicative noise term given …

The goal of this article is to investigate infinite dimensional affine diffusion processes on the
canonical state space. This includes a derivation of the corresponding system of Riccati …

We develop a limit theory for controlled path-dependent mean field stochastic partial
differential equations (SPDEs) within the semigroup approach of Da Prato and Zabczyk …

We provide necessary and sufficient conditions for stochastic invariance of finite
dimensional submanifolds for solutions of stochastic partial differential equations (SPDEs) in …

We provide necessary and sufficient conditions for stochastic invariance of finite
dimensional submanifolds for solutions of stochastic partial differential equations (SPDEs) in …

In this article we study the classical finite dimensional Ito formula from an infinite
dimensional perspective. A finite dimensional semi-martingale is represented as a semi …

We prove the martingale representation theorem for Brownian motion, with an explicit
expression for the integrand for random variables of the form. We introduce a new stochastic …

We prove limit theorems for cylindrical martingale problems associated with Lévy
generators. Furthermore, we give sufficient and necessary conditions for the Feller property …