Durrett R. Essentials of Stochastic Processes 2021

Textbook in PDF format

Building upon the previous editions, this textbook is a first course in stochastic processes taken by undergraduate and graduate students (MS and PhD students from math, statistics, economics, computer science, engineering, and finance departments) who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and option pricing. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding.
Note: this is the updated version of author's book "Essentials of Stochastic Processes" (3rd. ed., Springer, 2016)