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Preface to the Third Edition - Pg. xiii

Preface to the Third Edition The purposes, level, and style of this new edition conform to the tenets set forth in the original preface. We continue with our objective of introducing some theory and appli- cations of stochastic processes to students having a solid foundation in calculus and in calculus-level probability, but who are not conversant with the "epsilon­delta" def- initions of mathematical analysis. We hope to entice students toward the deeper study of mathematics that is prerequisite to further work in stochastic processes by showing the myriad and interesting ways in which stochastic models can help us understand the real world. We have removed some topics and added others. We added a small section on martingales that includes an example suggesting the martingale concept as appropriate for modeling the prices of assets traded in a perfect market. A new chapter introduces the Brownian motion process and includes several applications of it and its variants in financial modeling. In this chapter the Black­Scholes formula for option pricing is evaluated and compared with some reported prices of options. A Poisson process whose intensity is itself a stochastic process is described in another new section. Some treatments have been updated. The law of rare events is presented via an