Gregory F.Lawler talks about Stochastic Processes.

Emphasizing fundamental mathematical ideas rather than proof, the second edition provides quick access to important foundations of probability theory applicable to problems in many fields. The author approaches the problems and theorems with a focus on stochastic processes evolving with time, rather than a particular emphasis on measure theory, if you have a reasonable level of computer literacy, the ability to write simple programs, and the access to software for linear algebra computations.

The author begins with a brief introduction to the concepts of linear differential and difference equations. He talks about optimal stopping, martingales, and Brownian motion. The book ends with a chapter on integration. The exercises at the end of each chapter are provided by the author.

There is a new edition of the second edition. Modern mathematical finance is introduced in the expanded chapter on stochastic integration. The Feynman-Kac formula is introduced. There is an expanded discussion of the formula for pricing options. There is a discussion on self similarity in the chapter on Brownian motion.

This introduction is an excellent resource for both students and professionals and is applicable to the fields of mathematics, statistics, and engineering as well as computer science, economics, business, biological science, psychology, and engineering.