MA 262: Introduction to Stochastic Processes
Credits: 3:0
- Discrete parameter Markov Chains: Chapman-Kolmogorov equations, Classification of states, Limit Theorems, Examples: Random Walks, Gambler’s Ruin, Branching processes. Time reversible Markov chains. Simulations and MCMC (16 lectures)
- Poisson processes, Definitions, and properties: interarrival and waiting time distributions, superposition and thinning, Nonhomogeneous Poisson process, Compound Poisson process. Simulation. (5 lectures)
- Continuous time Markov Chains: Definition, Birth-Death processes, Kolmogorov backward and forward equations, Limiting probabilities, Time reversibility. Queueing Theory, Simulation. (10 lectures)
- Renewal Theory. (3 lectures)
- Brownian Motion. (6 lectures).
Suggested books and references:
- Karlin and Taylor, A first course in Stochastic Processes, Academic Press; 2nd edition, 1975.
- Sheldon Ross, Stochastic Processes, Wiley; 2nd edition, 2008.
- Bhattacharya and Waymire, Stochastic Processes and Applications, Society for Industrial and Applied Mathematics, 2009.