A weak invariance principle for Hilbert space valued martingales

Hilbert Space-valued Mixingales

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.

Stochastic Maximum Principle for Hilbert Space Valued Forward-Backward Doubly SDEs with Poisson Jumps

Independence of Four Projective Criteria for the Weak Invariance Principle

Let (Xi)i∈Z be a regular stationary process for a given filtration. The weak invariance principle holds under the condition ∑ i∈Z ‖P0(Xi)‖2 < ∞ (see [11], [2], [3]). In this paper, we show that this criterion is independent of other known criteria: the martingalecoboundary decomposition of Gordin (see [7], [8]), the criterion of Dedecker and Rio (see [4]) and the condition of Maxwell and Woodro...

A Note on Quadratic Maps for Hilbert Space Operators

In this paper, we introduce the notion of sesquilinear map on Β(H) . Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality...