Department of Statistics

Recent Instructors Kang, Min	ST (MA) 546	Probability and Stochastic Process
	Course Description Modern introduction to Probability Theory and Stochastic Processes. The choice of material is motivated by applications to problems such as queueing networks, filtering and financial mathematics. Topics include: review of discrete probability and continuous random variables, random walks, markov chains, martingales, stopping times, erodicity, conditional expectations, continuous-time Markov chains, laws of large numbers, central limit theorem and large deviations. Course Syllabus Probability space Sigma algebra Probability measure Discrete and continuous random variables Conditioning Independence Limit theorems in the context of independent random variables Random walks Random vectors Joint density Joint distribution Conditional density Conditional expectations Moment generating functions Characteristic functions Sums of independent random variables and limit theorems Laws of large numbers and central limit theorems Markov chains Course Prerequisites MA 425 or MA 511 MA 421 Course Corequisites None Recent Textbooks Advanced Probability Theory, 2nd ed., by Janos Galambos (1995)