Welcome to Introduction to Probability Theory and Stochastic Processes (Part B) !  Syllabus

 

 

 

 

Topics: Convergence of random variables: different types of convergence; characteristic functions, continuity theorem, laws of large numbers, central limit theorem, large deviations, infinitely divisible and stable distributions, uniform integrability. Conditional expectation.

Lecture : T/R 9:30-10:45 am GIRV 2119

Instructor: Tomoyuki Ichiba  (he/his/him) email: ichiba@pstat.ucsb.edu

Section : F 11-11:50 am ILP 4211

TA: Haosheng Zhou email: hzhou593@ucsb.edu

TA Office Hour: T 7:00 - 8:00 pm, Room 113, Building 434

TA Section Notes Available at: here

Prerequisites: PSTAT 213A, and either PSTAT 210 or Math 118 A-B-C

Instructor Office Hour: W 8:30-9 am, R 11-11:30 am, F 9-9:50 am South Hall 5508 or via zoom or different times by appointment

Textbook: Grimmett & Stirzaker (GS), Probability and Random Processes (we work based on the 3rd edition but now the 4th edition (2020) is available.)

References: 

Durrett, Probability: Theory and Example

Resnick, Adventures in Stochastic Processes 

Resnick, A Probability Path

Billingsley, Probability and Measure

Breiman, Probability

Jacod & Protter, Probability Essentials

 

Week 1 Convergence of functions and random variables (GS 7.1-7.3)

Week 2 Law of Large Numbers, Strong Law (GS 7.4-7.5) 

Week 3 Characteristic functions, Two limit Theorems (GS 5.7-5.10)

Week 4 Law of Iterated Logarithm, Conditional Expectation, Martingale, examples,  (GS 7.7-7.8)

Week 5 Midterm (February 6th), Martingale convergence, prediction and conditional expectation (GS 7.8-7.9)

Week 6 Uniform integrability (GS 7.10), Random processes (GS 8.1-8.2)

Week 7 Stationary process, Ergodic theorem (GS 9.1-9.5)

week 8 Gaussian process (GS 9.6), Concentration of measures, Large Deviations (GS 5.11)

week 9 Existence and uniqueness of process (GS 8.6), Infinitely divisible and stable distribution  

week 10 Application of topics, review and problem solving