721—Stochastic Processes. (3) (Prereq: STAT 811 or 712) Theory of stochastic processes, including branching processes, discrete and continuous time Markov chains, renewal theory, point processes, and Brownian motion.
Usually Offered: Fall odd years
Purpose: To acquaint graduate students with modern theory of stochastic processes and their use in modeling and statistical application.
Current Textbook: Adventures in Stochastic Processes (6th ed.) Sidney Resnick, Birkhäuser, Boston, 1992.
| Topics Covered | Time | |
| Review of probability concepts: Convolutions, generating functions, limit theory | 1 week | |
| Discrete Markov chains: Transition probabilities, state space decomposition, transient and recurrent chains, periodicity, absorption probabilities, stationary distributions, applications | 4 weeks | |
| Renewal theory: Counting renewals, the renewal equation, Poisson processes, queuing examples | 2.5 weeks | |
| Point processes: Poisson processes, nonhomogeneous Poisson processes | 2.5 weeks | |
| Continuous-time Markov processes: Stability, stationary and limiting distributions, Laplace transform methods, applications | 3 weeks | |
| Continuous processes: Gaussian processes, Brownian motions, the reflection principle, drift, applications | As time permits |
The above textbook and course outline should correspond to the most recent offering of the course by the Statistics Department. Please check with the instructor for the course regulations, expectations, and operating procedures.
Contact Faculty: Edsel Peña