This book is designed as a text for graduate courses in stochastic processes.
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.
Second Edition
I. Karatzas and S.E. Shreve
Brownian Motion and Stochastic Calculus
"A valuable book for every graduate student studying stochastic process, and for those who are interested in pure and applied probability. The authors have done a good job."―MATHEMATICAL REVIEWS