Stat 150: Stochastic Processes (Spring 2023)

Course information

Instructor: Benson Au
Lectures: MWF 1:10p-2:00p (Stanley 106)
Office hours: MF 2:00p-3:00p (443 Evans Hall)

GSI: Daniel Raban
Discussion section (optional): W 4:10p-5:00p (332 Evans Hall)
Office hours: Tu 2:00p-4:00p, W 5:00p-6:00p

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: Feb 27

Midterm #2: Apr 10

Final: Tuesday, 9 May, 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 Jan 23rd at 11:59 PM on Gradescope.

Homework 1 (.tex), due Jan 27 at 11:59 PM on Gradescope.

Homework 2, (.tex), due Feb 6 at 11:59 PM on Gradescope.

Homework 3, (.tex), due Feb 10 at 11:59 PM on Gradescope.

Homework 4, (.tex), due Feb 17 at 11:59 PM on Gradescope.

Homework 5, (.tex), due Feb 24 at 11:59 PM on Gradescope.

Homework 6, (.tex), due Mar 10 at 11:59 PM on Gradescope.

Homework 7, (.tex), due Mar 17 at 11:59 PM on Gradescope.

Homework 8, (.tex), due Mar 24 at 11:59 PM on Gradescope.

Homework 9, (.tex), due Apr 7 at 11:59 PM on Gradescope.

Homework 10, (.tex), due Apr 28 at 11:59 PM on Gradescope.

Homework 11, (.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 18: Outline of course, probability review (PK 1.1-1.6, D A.1-A.3)

Week 1, Jan 20: Conditional probability and conditional expectation (PK 2.1), Random sums (PK 2.3)

Week 2, Jan 23: Random sums (PK 2.3), Markov chains (PK 3.1, D 1.1-1.2)

Week 2, Jan 25: Markov chains (PK 3.1-3.3, D 1.1-1.2)

Week 2, Jan 27: Markov chains (PK 3.3-3.4, D 1.9-1.10)

Week 3, Jan 30: Markov chains (PK 3.3-3.6)

Week 3, Feb 1: Markov chains (PK 3.5-3.6), branching process (PK 3.8)

Week 3, Feb 3: Branching process (PK 3.9)

Week 4, Feb 6: Branching process (PK 3.9), Long-run behavior of Markov chains (PK 4.1)

Week 4, Feb 8: Long-run behavior of Markov chains (PK 4.1, 4.2)

Week 4, Feb 10: Long-run behavior of Markov chains (PK 4.2, 4.3)

Week 5, Feb 13: Long-run behavior of Markov chains (PK 4.3)

Week 5, Feb 15: Long-run behavior of Markov chains (PK 4.3. 4.4)

Week 5, Feb 17: Long-run behavior of Markov chains (PK 4.4)

Week 6, Feb 20: Presidents' Day

Week 6, Feb 22: Poisson process (PK 5.1, Durrett 2.1, 2.2)

Week 6, Feb 24: Poisson process (PK 5.1, Durrett 2.1, 2.2)

Week 7, Feb 27: Midterm 1

Week 7, Mar 1: Poisson process (PK 5.2)

Week 7, Mar 3: Poisson process (PK 5.3, Durrett 2.2)

Week 8, Mar 6: Poisson process (PK 5.4), Conditioning on a continuous random variable (assigned reading: PK 2.4)

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

Week 8, Mar 10: Poisson process (PK 5.4)

Week 9, Mar 13: Poisson process (D 2.4), Renewal process (PK 7.1)

Week 9, Mar 15: Renewal process (PK 7.2, 7.3)

Week 9, Mar 17: Renewal process (PK 7.3, Durrett 3.1)

Week 10, Mar 20: Renewal process (Durrett 3.1, PK 7.5)

Week 10, Mar 22: Renewal process (Durrett 3.1, 3.2, PK 7.5)

Week 10, Mar 24: Renewal process (Durrett 3.2, 3.3.2)

Week 11, Mar 27: Spring Recess

Week 11, Mar 29: Spring Recess

Week 11, Mar 31: Spring Recess, Cesar Chavez Day

Week 12, Apr 3: Renewal process (Durrett 3.3.2), Continuous time Markov chains (Durrett 4.1)

Week 12, Apr 5: Continuous time Markov chains (Durrett 4.1)

Week 12, Apr 7: Continuous time Markov chains (Durrett 4.1, 4.2)

Week 13, Apr 10: Midterm 2

Week 13, Apr 12: Continuous time Markov chains (Durrett 4.2)

Week 13, Apr 14: Continuous time Markov chains (Durrett 4.2)

Week 14, Apr 17: Continuous time Markov chains (Durrett 4.3)

Week 14, Apr 19: Continuous time Markov chains (Durrett 4.4)

Week 14, Apr 21: Continuous time Markov chains (Durrett 4.4), Martingales (Durrett 5.1)

Week 15, Apr 24: Martingales (Durrett 5.1, 5.2)

Week 15, Apr 26: Martingales (Durrett 5.3)

Week 15, Apr 28: Martingales (Durrett 5.3, 5.4.1)

Week 16, May 1: RRR week

Week 16, May 3: RRR week

Week 16, May 5: RRR week

Week 17, May 9: Final exam