632 - Introduction to Stochastic Processes
Prerequisites:
Math 431, or Stat 309 and 310, or Stat 311 and 312, or Stat 313 or 314.
Frequency:
Fall (I), Spring (II)
Student Body:
Advanced undergraduates and graduate students
Credits:
3. (N-A) Recent Texts:
Introduction to Stochastic Processes by Hoel, Port, and Stone, or Essentials of Stochastic Processes by Durrett
Course Coordinator:
David Anderson Background and Goals:
Math 632 gives an introduction to Markov chains and Markov processes with discrete state spaces and their applications. Particular models studied include birth-death chains, queuing models, random walks and branching processes. Selected topics from renewal theory and Brownian motion are also included, but vary from semester to semester to meet the needs of different audiences. Those looking for a similar course, though one with more of a focus on biological applications and computational methods, should look at Math 605.
Alternatives:
Math 605
Subsequent Courses:
Math 635, 735, 831-832 Course Content:
- Markov Chains
- transition functions and related computations
- classification of states: recurrence, transcience, irreducibility, periodicity
- examples: queuing, birth-death chains, branching, random walks
- Limiting Behavior of Markov Chains
- the main limit theorem and stationary distributions
- absorption probabilities
- further recurrence criteria
- Continuous Time Markov Chains
- definitions and examples (Poisson process)
- structure of a Markov process: waiting times and jumps
- the Kolmogorov differential equations
- limit theory
- birth-death processes and other examples
- Selected Topics
- renewal theory and applications
- a first look at Brownian motion and some applications