Three extra topics not covered this semester are renewal processes, queueing theory, and the connection between random walks and electrical networks. If unsure about your preparation, please discuss it with me. General proficiency in calculus and linear algebra. Prerequisite: An introductory probability course such as MATH 4710, BTRY 4080, ORIE 3600, ECON 3190. Brief introductions to the Metropolis-Hastings algorithm, Google PageRank, continuous time Markov chains, and Markov chain mixing times.Brownian motion: definition and construction, reflection principle, uncountability of the zero set.
Mathematical finance: arbitrage-free pricing, hedging, European and American options, Capital Asset Pricing Model, Black-Scholes formula.Stopping times, optional stopping theorems and applications. Martingales: gambling and prediction interpretations.Poisson process: exponential waiting times, memorylessness, thinning and superposition, conditioning.Markov chains: strong Markov property, transience and recurrence, irreducibility, periodicity, stationary distributions and convergence, exit times and distributions.Office hours: W 10 am - 12 pm, Malott Hall 210 Extra office hours: Friday, May 13, 1-3 pm, Malott Hall 210 Tuesday, May 17, 1-3 pm, Malott Hall 581Įmail: xq44 at Topics covered: Math 4740: Stochastic Processes Math 4740: Stochastic Processes Spring 2016 Basic information:
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