Girsanov's theorem in Hilbert space and an application to the statistics of Hilbert space- valued stochastic differential equations

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.

Hilbert Space-valued Mixingales

Differential Equations Driven by Lévy White Noise in Spaces of Hilbert-space-valued Stochastic Distributions

We develop a white noise framework and the theory of stochastic distribution spaces for Hilbert-space-valued Lévy processes. We then apply these concepts to the study of generalized solutions of stochastic evolution equations in these spaces driven by Lévy white noise.

Hilbert Space Methods for Partial Differential Equations

i Preface This book is an outgrowth of a course which we have given almost periodically over the last eight years. It is addressed to beginning graduate students of mathematics, engineering, and the physical sciences. Thus, we have attempted to present it while presupposing a minimal background: the reader is assumed to have some prior acquaintance with the concepts of " linear " and " continuo...

Projective Statistics and Spinors in Hilbert Space

In quantum mechanics, symmetry groups can be realized by projective, as well as by ordinary unitary, representations. For the permutation symmetry relevant to quantum statistics of N indistinguishable particles, the simplest properly projective representation is highly non-trivial, of dimension 2 N−1 2 , and is most easily realized starting with spinor geometry. Quasiparticles in the Pfaffian q...