Probabilistic and Stochastic Methods in Analysis, with Applications

Probability has been an important part of mathematics for more than 300 years. 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, all of which are covered in this volume. The book contains three expositions on wavelets, frames and their applications. The book also covers the relation between probability and partial differential equations, including probablistic 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 also explored. Another topic dealt with is the application of probablistic techniques to mathematical analysis. Finally, there are explanations of normal numbers and dynamic systems, and the influence of probability on our daily lives.