The study of stochastic processes is the application of probability to an indexed collection of random variables. A classic example is the study of queue times, an instance of which is wait times at the post office. Stochastic processes are very important for modeling, but they're also an important tool for other statistical methods. Much of Bayesian statistical estimation is based on Markov chain Monte Carlo, which is a kind of stochastic process.
Recommended Books

Adventures in Stochastic Processes
Sidney I. Resnick
Key Features
 Intext exercises
Key Topics
 Absorption Probabilities
 Branching Processes
 Brownian Motion
 ContinuousTime Markov Chains
 Discrete State Spaces
 Generating Functions
 Law of the Iterated Logarithm
 Markov Chains
 Point Processes
 Poisson Process
 Queueing
 Random Walks
 Renewal Theory
 Stationary and Limiting Distributions
 Stopping Times
 Transience and Recurrence
Description
This book has very clear explanations. We particularly appreciate the fact that results are presented in general matrix forms, as opposed to poncing around with the univariate case. Probability exercises tend to be entertaining as data science exercises go, and the antics of
Happy Harry
in this book are no exception. The asterisked enrichment sections in this book are quite interesting for the more mathematically inclined. 
Stochastic Processes
Sheldon M. Ross
Key Features
 Intext exercises
 Solutions to some exercises
Key Topics
 Birth and Death Processes
 Branching Processes
 Brownian Motion
 ContinuousTime Markov Chains
 Hazard Rates
 Markov Chains
 Martingales
 Point Processes
 Poisson Approximations
 Poisson Process
 Probability Review
 Queueing
 Random Walks
 Renewal Reward Processes
 Renewal Theory
 Stochastic Order Relations
Description
This is the standard text on stochastic processes. We find it somewhat vague in places and some of the results are not presented in as general a form as we would like. However, the exercises are quite good, and the book offers solutions to some of them. It's also geared at a slightly easier level than our top pick, so if you don't have a strong mathematical background you may prefer this book.