Eigenfunction expansions for infinite dimensional Ornstein-Uhlenbeck processes
We give a general construction of infinite dimensional Ornstein-Uhlenbeck processes. We present expansions of these processes based on the expansion of the covariance operators in generalized eigenfunctions, and we answer positively some question left open by \textit{J. B. Walsh} [Adv. Appl. Math. 13, 231-281 (1981; Zbl 0471.60083)] on properties of the hitting times of these processes.
infinite dimensional Ornstein-Uhlenbeck processes
scientific article; zbMATH DE number 3940358
scientific article