Continuity properties of Hilbert space valued martingales

Continuity of Measureson Hilbert Space

The paper considers continuity properties of a nite Borel measure on a separable Hilbert space X. Continuity of the mappings x 7 ! (A + x) on a subspace H, uniformly in A 2 B(X), is characterized by the existence of a nonstandard density of having a certain property. This generalizes a well known standard result for measures on R n. The ideas are illustrated with reference to Gaussian measures ...

Hilbert Space-valued Mixingales

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

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.

Some Continuity Properties of Brownian Motion with the Time Parameter in Hilbert Space,1) By

Levy introduced this process in [5, Chapter 8]. A bibliography of his later work is given in the second edition. The sample functions of this process are continuous when H is finite dimensional; however, when His infinite dimensional, the sample functions are not only discontinuous but also unbounded on every sphere. The local irregularity of the sample functions is caused by the property of in...