Offers selected topics in probability such as sums of independent random variables, notions of convergence, characteristic functions, Central Limit Theorem, random walk, conditioning and martingales, Markov chains and Brownian motion.
Ongoing course
Time: MWF 11:30 AM – 12:20 PM
Location: CLRE 208
Office hours: See details here
Grading
Homework: 30% – Weekly homework (you must turn them in)
Midterm: 30% – TBA
Final : 40% – TBA
Homework sets
All problems refer to our textbook.
Textbook
Some books that may be useful in this course
Course notes
Invariant Measures and Ergodic Theorem – MATH 6534
Invariant measures and its connections with return times. Ergodic Theorem.
Decomposition Theorem – MATH 6534
Recurrence is contagious, defining equivalence relation on the set of recurrent states. The Decomposition Theorem.
Recurrence and Transience – MATH 6534
Hitting times, recurrence and transience, and equivalent definitions.
Network analysis with martingales – MATH 6534
Investigating the Barabasi-Albert model with martingales.
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Rodrigo Ribeiro, Ph.D 