Introduction to Stochastic Processes I


Stanford School of Engineering

Statistics: Introduction to Stochastic Processes I


A stochastic process is a set of random variables indexed by time or space. Stochastic modelling is an interesting and challenging area of probability and statistics that is widely used in the applied sciences. In this course you will gain the theoretical knowledge and practical skills necessary for the analysis of stochastic systems. You will study the basic concepts of the theory of stochastic processes and explore different types of stochastic processes including Markov chains, Poisson processes and birth-and-death processes.

Non-Statistics master’s students may want to consider taking STATS 215 instead.

What you will learn

  • The standard concepts and methods of stochastic modeling
  • How to choose the best stochastic process for specific situations
  • How to apply stochastic analysis to realistic problems


  • Anthony D'Aristotile


A post-calculus introductory probability course, e.g. Stanford Course STATS116

Topics include

  • Discrete and continuous time Markov chains
  • First step analysis: gambler’s ruin and successful runs
  • Branching processes
  • Poisson processes
  • Birth-and-death processes
  • Long run behavior