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Department of Statistics

STAT 721

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

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