Nonparametric prediction of a Hilbert space valued random variable

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{...

Hilbert Space Valued Generalized Random Processes – Part Ii

Generalized random processes (GRPs) were classified as GRPs (I) and (II) in Part I of this paper. Now we focus our attention om GRPs (I), i.e. linear continuous mappings from a certain space of test functions to some space of classical or generalized random variables. The paper is organized in the following manner: In the introductory section (Section 1) we provide some basic terminology and no...

Zakai Equations for Hilbert Space Valued Processes*

versity A state process is described by either a discrete time Hilbert space valued process, or a stochastic differential equation in Hilbert space. The state is observed through a finite dimensional process. Using a change of measure and a Fusive theorem the Zakai equation is obtained in discrete or continuous time. A risk sensitive state estimate is also defined.

Central limit theorems for Hilbert-space valued random fields satisfying a strong mixing condition

In this paper we study the asymptotic normality of the normalized partial sum of a Hilbert-space valued strictly stationary random field satisfying the interlaced ρ-mixing condition.