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 PMLocation: CLRE 208Office hours: See details here
Grading
Homework: 30% – Weekly homework (you must turn them in)Midterm: 30% – TBAFinal : 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 its connections with return times. Ergodic Theorem.
3 de December de 2021
Recurrence is contagious, defining equivalence relation on the set of recurrent states. The Decomposition Theorem.
2 de December de 2021
Hitting times, recurrence and transience, and equivalent definitions.
22 de November de 2021
Simple and Strong Markov Properties and applications.
17 de November de 2021
Definition, the canonical chain and examples of markov chains.
15 de November de 2021
Azuma inequality.
11 de November de 2021
Investigating the Barabasi-Albert model with martingales.
11 de November de 2021
Martingales. Definition and convergence theorems.
11 de November de 2021
Conditional expectation.
8 de November de 2021 8 de November de 2021
Inversion formula, Continuity Theorem and the CLT.
2 de November de 2021
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