Stochastic differential equations in Hilbert space

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...

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.

Stochastic differential inclusions of semimonotone type in Hilbert spaces

In this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in F(t,x(t))dt +G(t,x(t))dW_t$ in which the multifunction $F$ is semimonotone and hemicontinuous and the operator-valued multifunction $G$ satisfies a Lipschitz condition. We define the It^{o} stochastic integral of operator set-valued stochastic pr...

Stochastic Partial Differential Equations and Submanifolds in Hilbert Spaces

The goal of this appendix is to provide results about stochastic partial differential equations driven by Wiener processes and Poisson measures and results about submanifolds in Hilbert spaces. It should serve as a reference for auxiliary results that we require in [7].

On Some Fractional Stochastic Integrodifferential Equations in Hilbert Space