Stochastic Processes

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Stochastic Processes written by Richard F. Bass aims to provide a complete overview of stochastic processes. This book is ambitious in the breadth of ground it covers but it is nevertheless a valuable resource for a variety of readerships, including graduate students and researchers who are interested in this subject matter. In my view, to fully appreciate the material developed, the readers require familiarity with the theory and techniques studied during an undergraduate or perhaps a graduate probability course, including basic measure theory. As such, the book is not suitable as an introduction for someone completely unfamiliar with the mathematical and probabilistic concepts that underpin the theory of stochastic processes, there are likely other books better suited to that purpose.

The 42 chapters of the book can be grouped into 7 parts:

Part 1 introduces the basic tools for analysis stochastic processes, focusing on Brownian motion definition, construction and properties.

Part 2 looks at the theory of stochastic calculus, including stochastic integrals and Itô's formula.

Part 3 is concerned with jump processes based on foundations of stochastic processes.

Part 4 addresses Markov processes, their applications and transformations.

Part 5 outlines stochastic differential equations, with two important applications: the Black- Scholes formula for pricing of derivatives in financial...