**Instructor:** Benson Au

**Lectures:** MWF 10:10a-11:00a (Cory 277)

**Office hours:**

- W 11:30a-12:30p (Zoom link on bCourses)
- F 12:30p-1:30p (Zoom link on bCourses)

**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)

Please bring your student ID to the exams.

**Midterm #1:** Monday, Oct 4th, during lecture

**Midterm #2:** Monday, Nov 8th, during lecture

**Final:** Monday, Dec 13th, 8:00a-11:00a in Cory 277

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 September 3rd at 11:59 PM on Gradescope.

Homework 1 (.tex), due September 10th at 11:59 PM on Gradescope.

Homework 2, (.tex), due September 24th at 11:59 PM on Gradescope.

Homework 3, (.tex), due September 24th at 11:59 PM on Gradescope.

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

Homework 5, (.tex), due October 15th at 11:59 PM on Gradescope.

Homework 6, (.tex), due October 25th at 11:59 PM on Gradescope.

Homework 7, (.tex), due November 8th at 11:59 PM on Gradescope.

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

Homework 9, (.tex), due November 19th at 11:59 PM on Gradescope.

Extra credit, (.tex), due November 19th at 11:59 PM on Gradescope.

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

Homework 11, (.tex), not due.

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, Aug 25: Probability review (PK 1.1-1.6, D A.1-A.3)

Week 1, Aug 27: Probability review (PK 1.1-1.6, D A.1-A.3)

Week 2, Aug 30: Probability review (PK 1.1-1.6, D A.1-A.3)

Week 2, Sep 1: Convolution, Gamma distribution, Conditional probability and conditional expectation (PK 1.2.5, 1.4.4, 2.1)

Week 2, Sep 3: Conditional expectation, Random sums (PK 2.1, 2.3)

Week 3, Sep 6: Labor day

Week 3, Sep 8: Markov chains (PK 3.1-3.3)

Week 3, Sep 10: Markov chains (PK 3.4)

Week 4, Sep 13: Markov chains (PK 3.5)

Week 4, Sep 15: Markov chains (PK 3.6)

Week 4, Sep 17: Markov chains (PK 3.8-3.9)

Week 5, Sep 20: Markov chains (PK 4.1)

Week 5, Sep 22: Markov chains (PK 4.2)

Week 5, Sep 24: Markov chains (PK 4.3)

Week 6, Sep 27: Markov chains (PK 4.3, 4.4)

Week 6, Sep 29: Markov chains (PK 4.4)

Week 6, Oct 1: Poisson process (PK 5.1)

Week 7, Oct 4: Midterm #1

Week 7, Oct 6: Poisson process (PK 5.2)

Week 7, Oct 8: Poisson process (PK 5.2)

Week 8, Oct 11: Poisson process (PK 5.2, 5.3)

Week 8, Oct 13: Poisson process (PK 5.3, 5.4)

Week 8, Oct 15: Poisson process (PK 5.4)

Week 9, Oct 18: Poisson process (PK 5.4), Conditioning on a continuous random variable (PK 2.4)

Week 9, Oct 20: Pure birth processes (PK 6.1)

Week 9, Oct 22: Pure birth processes (PK 6.1)

Week 10, Oct 25: Pure death processes (PK 6.2)

Week 10, Oct 27: Birth and death processes (PK 6.3)

Week 10, Oct 29: Limiting behavior of birth and death processes (PK 6.4)

Week 11, Nov 1: Birth and death processes with absorbing states (PK 6.5)

Week 11, Nov 3: Finite-state continuous time Markov chains (PK 6.6)

Week 11, Nov 5: Review/catch-up

Week 12, Nov 8: Midterm #2 (on Poisson process, Chapter 5 of PK, and continuous time Markov chains, Chapter 6 of PK)

Week 12, Nov 10: Renewal process (PK 7.1)

Week 12, Nov 12: Renewal process (PK 7.2, 7.3)

Week 13, Nov 15: Renewal process (PK 7.4)

Week 13, Nov 17: Renewal process (PK 7.4, D 3.1)

Week 13, Nov 19: Renewal process (PK 7.4, D 3.1)

Week 14, Nov 22: Renewal process (PK 7.4, D 3.3.2)

Week 14, Nov 24: Non-instructional day

Week 14, Nov 26: Thanksgiving

Week 15, Nov 29: The multivariate normal distribution

Week 15, Dec 1: Brownian motion (PK 8.1)

Week 15, Dec 3: Brownian motion (PK 8.2)

Week 16, Dec 6: RRR week

Week 16, Dec 8: RRR week

Week 16, Dec 10: RRR week

Week 17, Dec 13: Final exam