An introduction to continuous-time stochastic processes : theory, models, and applications to finance, biology, and medicine / Vincenzo Capasso, David Bakstein

This is an introductory text on continuous time stochastic processes and their applications to finance and biology. The first part of the book reviews basic probability and then covers the basic continuous time processes such as Brownian motion, point processes, etc. It then introduces the Itô integral and Itô formula, and develops the basic theory of stochastic differential equations, inclusive of Lyapunov-type stability criteria. Proofs that are very technical are omitted.
The second part of the book deals with applications. The chapter on finance and insurance covers option pricing, interest rate models and insurance risk. The chapter on biology and medicine considers a variety of models of population dynamics and an application to neurosciences.
Four appendices cover the background from analysis required in the book, viz., measure and integration, probability measures on metric spaces, elliptic and parabolic p.d.e.'s, and stability theory for ordinary differential equations.
The book will be useful for applied mathematicians who are not probabilists to get a quick flavour of the techniques of stochastic calculus, and for professional probabilists to get a quick flavour of the applications. (MathScinet)