Stat 150: Stochastic Processes (Spring 2022)

Course information

Instructor: Benson Au
Lectures: MWF 1:10p-2:00p (Stanley 106)
Office hours: TBD over Zoom (link on bCourses)

GSI: Yassine El Maazouz
Discussion sections: TBD
Office hours: TBD

Textbooks:

An Introduction to Stochastic Modeling by Pinsky and Karlin (freely available through the university library here)
Essentials of Stochastic Processes by Durrett (freely available through the university library here)

To reiterate, the textbooks are freely available through the university. Note that you must be connected to the university Wi-Fi or VPN to access the ebooks from the library links. Furthermore, the library links take some time to populate, so do not be alarmed if the webpage looks bare for a few seconds.

Exam schedule

Please bring your student ID to the exams.

Midterm #1: Mon, Feb 28th, in class

Midterm #2: TBD

Final: Tuesday, May 10th, 8:00a-11:00a in TBD

Homework assignments

PK refers to Pinksy and Karlin. D refers to Durrett. Note that there are both exercises and problems in PK. Make sure you are doing the correct assignment.

Homework 0, due Mon, Jan 24th, at 11:59 PM on Gradescope.

Homework 1 (.tex), due Fri, Feb 4th, at 11:59 PM on Gradescope.

Homework 2, (.tex), due Fri, Feb 11th, at 11:59 PM on Gradescope.

Homework 3, (.tex), due Fri, Feb 18th at 11:59 PM on Gradescope.

Homework 4, (.tex), due Mon, Feb 28th at 11:59 PM on Gradescope.

Homework 5, (.tex), due Fri, Mar 11th at 11:59 PM on Gradescope.

Homework 6, (.tex), due Fri, Mar 18th at 11:59 PM on Gradescope.

Homework 7, (.tex), due Fri, April 1st at 11:59 PM on Gradescope.

Homework 8, (.tex), due Fri, April 8th at 11:59 PM on Gradescope.

Homework 9, (.tex), due Mon, April 25th at 11:59 PM on Gradescope.

Homework 10, (.tex), NOT DUE.

Course Calendar

The following calendar is subject to revision during the term. The section references are only a guide: our pace may vary from it somewhat. PK refers to Pinksy and Karlin. D refers to Durrett.

Week 1, Jan 19: Outline of course, probability review (PK 1.1-1.6, D A.1-A.3)

Week 1, Jan 21: Probability review (PK 1.1-1.6, D A.1-A.3)

Week 2, Jan 24: Conditional probability and conditional expectation (PK 2.1)

Week 2, Jan 26: Conditional expectation, Random sums (PK 2.1, 2.3)

Week 2, Jan 28: Markov chains (PK 3.1, D 1.1-1.2)

Week 3, Jan 31: Markov chains (PK 3.1, 3.2, 3.3, D 1.1-1.2)

Week 3, Feb 2: Markov chains (PK 3.3, 3.4, D 1.1)

Week 3, Feb 4: Markov chains (PK 3.4)

Week 4, Feb 7: Markov chains (PK 3.5, 3.6)

Week 4, Feb 9: Branching process (PK 3.8)

Week 4, Feb 11: Branching process (PK 3.9)

Week 5, Feb 14: Long-run behavior of Markov chains (PK 4.1, 4.2)

Week 5, Feb 16: Long-run behavior of Markov chains (PK 4.3)

Week 5, Feb 18: Long-run behavior of Markov chains (PK 4.3, 4.4)

Week 6, Feb 21: Presidents' Day

Week 6, Feb 23: Long-run behavior of Markov chains (PK 4.4)

Week 6, Feb 25: Poisson process (PK 5.1, Durrett 2.1, 2.2)

Week 7, Feb 28: Midterm 1

Week 7, Mar 2: Poisson process (PK 5.2, 5.3)

Week 7, Mar 4: Poisson process (PK 5.3, Durrett 2.2)

Week 8, Mar 7: Poisson process (PK 5.3, 5.4, Durrett 2.2)

Week 8, Mar 9: Poisson process (PK 5.4)

Week 8, Mar 11: Poisson process (Durrett 2.4), Conditioning on a continuous random variable (assigned reading: PK 2.4)

Week 9, Mar 14: Renewal process (PK 7.1)

Week 9, Mar 16: Renewal process (PK 7.2, 7.3)

Week 9, Mar 18: Renewal process (PK 7.3, Durrett 3.1)

Week 10, Mar 21: Spring Recess

Week 10, Mar 23: Spring Recess

Week 10, Mar 25: Spring Recess, Cesar Chavez Day

Week 11, Mar 28: Renewal process (Durrett 3.1, PK 7.5)

Week 11, Mar 30: Renewal process (Durrett 3.1, 3.2, PK 7.5)

Week 11, Apr 1: Renewal process (Durrett 3.2, 3.3.2)

Week 12, Apr 4: Renewal process (Durrett 3.3.2), Continuous time Markov chains (Durrett 4.1)

Week 12, Apr 6: Continuous time Markov chains (Durrett 4.1)

Week 12, Apr 8: Continuous time Markov chains (Durrett 4.1, 4.2)

Week 13, Apr 11: Midterm 2

Week 13, Apr 13: Continuous time Markov chains (Durrett 4.2)

Week 13, Apr 15: Continuous time Markov chains (Durrett 4.2)

Week 14, Apr 18: Continuous time Markov chains (Durrett 4.3)

Week 14, Apr 20: Continuous time Markov chains (Durrett 4.4)

Week 14, Apr 22: Continuous time Markov chains (Durrett 4.4), Martingales (Durrett 5.1)

Week 15, Apr 25: Martingales (Durrett 5.1, 5.2, 5.3)

Week 15, Apr 27: Martingales (Durrett 5.3)

Week 15, Apr 29: Martingales (Durrett 5.3, 5.4.1)

Week 16, May 2: RRR week

Week 16, May 4: RRR week

Week 16, May 6: RRR week

Week 17, May 10: Final exam