The aim of this book is to be a self-contained, practical, entry level text on stochastic processes and control for jump-diffusions in continuous time, technically Markov processes
in continuous time.
The book is intended for graduate students as well as a research monograph for researchers in applied mathematics, computational science and engineering. Also, the book may be useful for financial engineering practicians who need fast and efficient answers to stochastic financial problems. Hence, the exposition is based upon integrated basic principles of applied mathematics, applied probability and computational science. The target audience includes mathematical modelers and students in many areas of science and engineering seeking to construct models for scientific applications subject to uncertain environments. The prime interest is in modeling and problem solving. The utility of the exposition, based upon systematic derivations along with essential proofs in the spirit of classical applied mathematics, is more important to setting up a stochastic model of an application than abstract theory. However, a lengthy last chapter is intended to bridge the gap between the applied world and the abstract world in order to enable applied students and readers to understand the more abstract literature.
For optimal use of this book, it would be helpful to have had prior introduction to applied probability theory including continuous random variables
, mathematical analysis at least at the level of advanced calculus. Ordinary differential equations, partial differential equations and basic computational methods would be helpful but the book does not rely on prior knowledge of these topics by using basic calculus style motivations. In other words, the more or less usual preparation for students of applied mathematics, science and engineering should be sufficient. However, the author has strived to make this book as self-contained as practical, not strongly relying on prior knowledge and explaining or reviewing the prerequisite knowledge at the point it is needed to justify a step in the systematic derivation of some mathematical result.