18.445
Introduction to Stochastic Processes
Spring 2015
Topics
- Introduction to Finite Markov Chains
- Markov Chains: Stationary Distribution
- Markov Chains: Time-reversal
- Introduction to Markov Chain Mixing
- Stationary Times
- Lower Bounds on Mixing Times
- Summary on Mixing Times
- Random Walk on Networks 1
- Random Walk on Networks 2
- Hitting Times
- Summary on Random Walk on Networks
- Countable State Space Chain 1
- Countable State Space Chain 2
- Conditional Expectation and Introduction to Martingales
- Martingales: Optional Stopping Theorem
- Martingales: Convergence
- Martingales: Uniformly Integrable
- Galton-Watson Tree
- Poisson Process
- Continuous Time Markov Chain
- Infinitesimal Generator
- Irreducible and Recurrence
- Stationary Distribution
Readings
- Williams, D. Probability with Martingales . Cambridge University Press, 1991. ISBN: 9780387985091.
Sources
- Course catalogue ↗Historical OpenCourseWare
- MIT OCW calendar ↗
- MIT OCW syllabus ↗
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.