This monograph, now in a thoroughly revised second edition, develops the
theory of stochastic calculus in Hilbert spaces and applies the results
to the study of generalized solutions of stochastic parabolic equations.
The emphasis lies on second-order stochastic parabolic equations and
their connection to random dynamical systems. The authors further
explore applications to the theory of optimal non-linear filtering,
prediction, and smoothing of partially observed diffusion processes. The
new edition now also includes a chapter on chaos expansion for linear
stochastic evolution systems.
This book will appeal to anyone working in disciplines that require
tools from stochastic analysis and PDEs, including pure mathematics,
financial mathematics, engineering and physics.