Topics: Markov chains: definition, transition probabilities, special Markov chains (random walks, dams and inventories, branching processes), classification of states, limit theorems. Poisson processes: derivations, homogeneous, non-homogeneous processes, spacial and marked Poisson processes. Continuous time Markov chains: the Chapman-Kolmogorev equation, birth and death processes, the case of a finite state space, special cases, limiting behavior. Renewal processes: definition, the renewal function, replacement models, renewal theorems, inspection paradox, applications. Brownian motions: definition, processes with independent increments, the maximum variable and the reflection principle, Brownian bridge, geometric Brownian motion, applications in modern financial theory. Queueing theory: queueing systems, Little˘s formula, Poisson arrivals and exponential and general service times, the case of an infinite number of servers, priority queues, queueing systems.
Prerequisites: Probability Theory
Returning in Fall 2008
H. M. Taylor and S. Karlin, An Introduction to Stochastic Modeling, 3rd edition, Academic Press
(We do not currently have a syllabus available for posting.)
Previous semesters:
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Updated 1/2008
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