This book is based on research that, to a large extent, started around
1990, when a research project on fluid flow in stochastic reservoirs was
initiated by a group including some of us with the support of VISTA, a
research coopera- tion between the Norwegian Academy of Science and
Letters and Den norske stats oljeselskap A.S. (Statoil). The purpose of
the project was to use stochastic partial differential equations (SPDEs)
to describe the flow of fluid in a medium where some of the parameters,
e.g., the permeability, were stochastic or "noisy". We soon realized
that the theory of SPDEs at the time was insufficient to handle such
equations. Therefore it became our aim to develop a new mathematically
rigorous theory that satisfied the following conditions. 1) The theory
should be physically meaningful and realistic, and the corre- sponding
solutions should make sense physically and should be useful in
applications. 2) The theory should be general enough to handle many of
the interesting SPDEs that occur in reservoir theory and related areas.
3) The theory should be strong and efficient enough to allow us to solve
th, se SPDEs explicitly, or at least provide algorithms or
approximations for the solutions.