Wiener-Itô Chaos Expansion of Hilbert Space Valued Random Variables

Ocone formula for vector valued random variables in abstract Wiener space

The classical representation of random variables as the Itô integral of nonanticipative integrands is extended to include Banach space valued random variables on an abstract Wiener space equipped with a filtration induced by a resolution of the identity on the Cameron–Martin space. The Itô integral is replaced in this case by an extension of the divergence to random operators, and the operators...

The Clark–ocone Formula for Vector Valued Random Variables in Abstract Wiener Space

Erratum to " The Clark-Ocone formula for vector valued random variables in abstract Wiener space " , Jour. In this paper we considered the extension of the Clark-Ocone formula for a random variable defined on an abstract Wiener space (W, H, µ) and taking values in a Banach space (denoted there either B or Y). The main result appears in Theorem 3.4. Unfortunately, as first pointed out to us by J...

Bootstrap for dependent Hilbert space-valued random variables with application to von Mises statistics

Statistical methods for functional data are of interest for many applications. In this paper, we prove a central limit theorem for random variables taking their values in a Hilbert space. The random variables are assumed to be weakly dependent in the sense of near epoch dependence, where the underlying process fulfills some mixing conditions. As parametric inference in an infinite dimensional s...

Hilbert Space-valued Mixingales

Hilbert Space Valued Generalized Random Processes – Part I

Generalized random processes by various types of continuity are considered and classified as generalized random processes (GRPs) of type (I) and (II). Structure theorems for Hilbert space valued generalized random processes are obtained: Series expansion theorems for GRPs (I) considered as elements of the spaces L(A, S(H)−1) are derived, and structure representation theorems for GRPs (II) on K{...