Bernt Oksendal 
Stochastic Differential Equations [PDF ebook] 
An Introduction with Applications

From the reviews to the first edition:Most of the literature about stochastic differentialequations seems to place so much emphasis on rigor andcompleteness that it scares the nonexperts away. These notesare an attempt to approach the subject from the nonexpertpoint of view.: Not knowing anything … about a subject tostart with, what would I like to know first of all. Myanswer would be: 1) In what situations does the subjectarise ? 2) What are its essential features? 3) What are theapplications and the connections to other fields?" Theauthor, a lucid mind with a fine pedagocical instinct, haswritten a splendid text that achieves his aims set forwardabove. He starts out by stating six problems in theintroduction in which stochastic differential equations playan essential role in the solution. Then, while developingstochastic calculus, he frequently returns to these problemsand variants thereof and to many other problems to show howthetheory works and to motivate the next step in thetheoretical development. Needless to say, he restrictshimself to stochastic integration with respectto Brownianmotion. He is not hesitant to give some basic resultswithout proof in order to leave room for "some more basicapplications"… It can be an ideal text for a graduate course, but it isalso recommended to analysts (in particular, those workingin differential equations and deterministic dynamicalsystems and control) who wish to learn quickly whatstochastic differential equations are all about. From: Acta Scientiarum Mathematicarum, Tom 50, 3-4, 1986