Diffusions, Markov Processes and Martingales: Ito Calculus (Wiley Series in Probability and Mathematics Statistics)

The main themes of this book are stochastic integrals, stochastic differential equations, excursion theory and 'the general theory of processes'. Much effort has gone into the attempt to make these subjects accessible by providing many concrete examples illustrating techniques of calculation, and by treating all topics (including stochastic differential geometry) from the ground up, starting from the simplest case. In particular, the theory is developed first for the 'continuous' case, by far the most important in practice, while the general theory (and its applications) forms the last chapter. Many of the examples and many of the proofs are new and some important methods of calculation appear for the first time in a book. Stochastic differential equations are widely used in practice: in electrical engineering; in controlling systems subject to random 'noise'; in modelling economic systems; and in several branches of physics and chemistry. They are also used to great effect in other branches of mathematics, such as the theory of partial differential equations, differential geometry and complex analysis. Researchers and practitioners in all these fields will find it a useful and highly readable reference work.