Probability has been an important part of mathematics for more than
three centuries. Moreover, its importance has grown in recent decades,
since the computing power now widely available has allowed probabilistic
and stochastic techniques to attack problems such as speech and image
processing, geophysical exploration, radar, sonar, etc. -- all of which
are covered here.
The book contains three exceptionally clear expositions on wavelets,
frames and their applications. A further extremely active current
research area, well covered here, is the relation between probability
and partial differential equations, including probabilistic
representations of solutions to elliptic and parabolic PDEs. New
approaches, such as the PDE method for large deviation problems, and
stochastic optimal control and filtering theory, are beginning to yield
their secrets. Another topic dealt with is the application of
probabilistic techniques to mathematical analysis. Finally, there are
clear explanations of normal numbers and dynamic systems, and the
influence of probability on our daily lives.