Recent Advances in Stochastic Calculus

This volume includes the material presented in the Distinguished Lecture Series on Stochastic Calculus at the Systems Research Center of the University of Maryland at College Park in 1987. The purpose of these lecture series and the volume is to acquaint a wide audience with certain recent advances in stochastic calculus and with their applications to significant problems. Stochastic systems play a fundamental role in automation and information en­ gineering. The analysis of stochastic systems depends in a fundamental way on stochastic calculus. The subject matter is rather sophisticated, requiring a broad mathematical sophistication and maturity. Yet improper understanding or utilization of stochastic calculus in applications, especially in engineering, can lead to incorrect numerial results and faulty designs. The material included in this volume appears for the first time in book form. Considerable effort was undertaken by the authors to present the material in a form accessible to as wide an audience as possible. Some of the material appears here for the first time, while we believe that the targeted tutorial and survey nature of some of the chapters should be extremely helpful to researchers studying recent developments in stochastic calculus. The topics were selected to cover some of the most important areas for stochastic control, stochastic filtering and stochastic modeling.

1. Filtering and control for point process observations.- 2. Non linear filtering theory.- 3. An introduction to Malliavin Calculus and some of its applications.- 4. Stochastic calculus on manifolds with applications.- 5. Controlled Markov chains on a countable state space: some recent results.- 6. Martingale problems for constrained Markov problems.- 7. Applications of stochastic calculus in financial economics.