非常有用的一本书
Book Description
This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic
probability and discrete-time processes who wish to explore stochastic processes in continuous time. The vehicle chosen for this
exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with
continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed. The power of this calculus
is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn
permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization).
This book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time
for semimartingales, with special emphasis on the theory of Brownian local time. The text is complemented by a large number of
problems and exercises.