Stat 150: Stochastic Processes (Spring 2024)

Course information

Instructor: Benson Au
Lectures: MWF 1:10p-2:00p (Stanley 106)
Office hours: M 2p-3p (422 Evans), F 4p-5p (443 Evans)

GSI: Ella Hiesmayr
Discussion section (optional): Tu 10a-11a (340 Evans)
Office hours: Tu 3:30p-5p, Th 11a-12:30p (428 Evans)

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 26

Midterm #2: TBA

Final: Tuesday, 7 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 22nd at 11:59 PM on Gradescope.

Homework 1 (.tex), due Jan 26 at 11:59 PM on Gradescope.

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

Homework 3, (.tex), due Feb 9 at 11:59 PM on Gradescope.

Homework 4, (.tex), due Feb 16 at 11:59 PM on Gradescope.

Homework 5, (.tex), due Feb 23 at 11:59 PM on Gradescope.

Homework 6, (.tex), due Mar 8 at 11:59 PM on Gradescope.

Homework 7, (.tex), due Mar 15 at 11:59 PM on Gradescope.

Homework 8, (.tex), due Mar 22 at 11:59 PM on Gradescope.

Homework 9, (.tex), due Apr 5 at 11:59 PM on Gradescope.

Homework 10, (.tex), due Apr 22 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 17: Outline of course, Conditional probability and conditional expectation (PK 2.1), Random sums (PK 2.3)
Reading: probability review as needed (PK 1.1-1.6, D A.1-A.3)

Week 1, Jan 19: Random sums (PK 2.3), Markov chains (PK 3.1, D 1.1-1.2)

Week 2, Jan 22: Markov chains (PK 3.1-3.3, D 1.1-1.2)

Week 2, Jan 24: Markov chains (PK 3.3-3.4, D 1.9-1.10)

Week 2, Jan 26: Markov chains (PK 3.3-3.6)

Week 3, Jan 29: Markov chains (PK 3.5-3.6)

Week 3, Jan 31: Branching process (PK 3.8)

Week 3, Feb 2: Branching process (PK 3.9)

Week 4, Feb 5: Long-run behavior of Markov chains (PK 4.1, 4.2)

Week 4, Feb 7: Long-run behavior of Markov chains (PK 4.2)

Week 4, Feb 9: Long-run behavior of Markov chains (PK 4.2, 4.3)

Week 5, Feb 12: Long-run behavior of Markov chains (PK 4.3)

Week 5, Feb 14: Long-run behavior of Markov chains (PK 4.4)

Week 5, Feb 16: Long-run behavior of Markov chains (PK 4.4)

Week 6, Feb 19: Presidents' Day

Week 6, Feb 21: Poisson process (PK 5.1)

Week 6, Feb 23: Poisson process (PK 5.2)

Week 7, Feb 26: Midterm 1

Week 7, Feb 28: Poisson process (PK 5.2, Durrett 2.1, 2.2)

Week 7, Mar 1: Poisson process (PK 5.3, Durrett 2.2)

Week 8, Mar 4: Poisson process (PK 5.4), Conditioning on a continuous random variable (assigned reading: PK 2.4)

Week 8, Mar 6: Poisson process (PK 5.4)

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

Week 9, Mar 11: Poisson process (Durrett 2.4.1, 2.4.2)

Week 9, Mar 13: Renewal process (Durrett 3.1)

Week 9, Mar 15: Renewal process (Durrett 3.1, PK 7.5)

Week 10, Mar 18: Renewal process (Durrett 3.2, PK 7.3)

Week 10, Mar 20: Renewal process (Durrett 3.3.2)

Week 10, Mar 22: Continuous time Markov chains (Durrett 4.1)

Week 11, Mar 25: Spring Recess

Week 11, Mar 27: Spring Recess

Week 11, Mar 29: Spring Recess, Cesar Chavez Day

Week 12, Apr 1: Continuous time Markov chains (Durrett 4.1)

Week 12, Apr 3: Continuous time Markov chains (Durrett 4.1, 4.2)

Week 12, Apr 5: Continuous time Markov chains (Durrett 4.2)

Week 13, Apr 8: Midterm 2

Week 13, Apr 10: Continuous time Markov chains (Durrett 4.3)

Week 13, Apr 12: Continuous time Markov chains (Durrett 4.3, 4.4)

Week 14, Apr 15: Continuous time Markov chains (Durrett 4.4), Martingales (Durrett 5.1)

Week 14, Apr 17: Martingales (Durrett 5.1)

Week 14, Apr 19: Martingales (Durrett 5.2)

Week 15, Apr 22: Martingales (Durrett 5.2, 5.3)

Week 15, Apr 24: Martingales (Durrett 5.3)

Week 15, Apr 26: Martingales (Durrett 5.3, 5.4.1)

Week 16, Apr 29: RRR week

Week 16, May 1: RRR week

Week 16, May 3: RRR week

Week 17, May 7: Final exam