## STAT 150: Stochastic Processes (Spring 2015)

** Practice Final:** pdf Solutions

** Midterm 1:** Solutions ** Midterm 2:** Solutions
** Practice Midterm 1:** Solutions ** Midterm 2:** Solutions

** RRR Week Schedule:**

Monday 12-1, 150 GSPP Review Session

Monday Section as usual

Tuesday 12-1 Leconte 0003 Problem Session with Jonathan

Wednesday 12-1, 150 GSPP Jonathan will go over the practice final solutions

**New**:Thursday 11-12:30 Evans 344 I will be giving an extra problem session

Office hours as usual

**New: Piazza:** [Signup]

**Instructor:** Allan Sly

**Course Syllabus:** Syllabus

**Class Time:** MWF 12:00 - 1:00 PM in room 150 Goldman School of Public Policy .

**Section:** Monday 3:00 - 4:00 PM or 4:00 - 5:00PM 332 Evans Hall.

**GSI: ** Jonathan Hermon.

**Office Hours ** Instructor: Tuesday 3:30-4:30 and Tuesday 10:30-11:30 Evans Hall 333.

GSI: Wednesday 5-7 and Friday 3-5 Evans 444.

**Email ** Instructor: sly@stat (with the obvious ending)

GSI: (jonathan.hermon@stat)

**Midterms ** Wednesday February 25 and April 8 in class.

**Exam ** May 13, 3:00-6:00PM

### Schedule

*Lecture 1, January 21: * Course introduction and Review of Stat 134 material.

*Lecture 2, January 23: * Review of Stat 134 material continued - random variables and conditional probabilities and expectations.

*Lecture 3, January 26: * Wald's Identity. See Pitman's [notes] .

*Lecture 4, January 28: * Martingales. See Pitman's [notes] .

*Lecture 5, January 30: * Markov Chains. See Pitman's [notes] or Section 4.1 of Gallager.

*Lecture 6, February 2: * Markov Chains continued.

*Lecture 7, February 4: * Long run behaviour of Markov chains. Notes by Pitman [notes] , [notes2] or Section 4.1 of Gallager 4.2 and 4.3.

*Lecture 8, February 6: * Long run behaviour of Markov chains continued.

*Lecture 9, February 9: * Long run behaviour of Markov chains continued.

*Lecture 10, February 11: * Long run behaviour of Markov chains continued.

*Lecture 11, February 13: * Long run behaviour of Markov chains continued, birth and death chains.

*Lecture 12, February 18: * First step analysis. Notes by Pitman [notes] , [notes2]

*Lecture 13, February 20: * First step analysis continued.

*Lecture 14, February 23: * Markov Chain Monte Carlo MCMC Notes .

*Lecture 15, February 25: * Midterm.

*Lecture 16, February 27: * Markov Chain Monte Carlo continued.

*Lecture 17, March 2: * Generating functions. Notes by Pitman [notes]

*Lecture 18, March 4: * Branching Processes. Notes by Pitman [notes]

*Lecture 19, March 6: * Branching Processes continued.

*Lecture 20, March 9: * Poisson Processes. Notes by Pitman [notes]

*Lecture 21, March 11: * Poisson Processes.

*Lecture 22, March 13: * Poisson Processes.

*Lecture 23, March 16: * Poisson Processes

*Lecture 24, March 18: * Continuous time Markov Chains. Notes by Pitman [notes] and [notes]

*Lecture 25, March 20: * Continuous time Markov Chains.

*Lecture 26, March 30: * Continuous time Markov Chains.

*Lecture 27, April 1: * Continuous time Markov Chains.

*Lecture 28, April 3: * Continuous time Markov Chains.

*Lecture 29, April 6: * Queueing Theory. Notes by Pitman [notes]

*Lecture 30, April 8: * Midterm

*Lecture 31, April 10: * Renewal Theory. Notes by Pitman [notes]

*Lecture 32, April 13: * Renewal Theory.

*Lecture 33, April 15: * Gaussian Processes.

*Lecture 34, April 17: * Brownian Motion. Notes by Pitman [notes] and [notes] .

*Lecture 35, April 20: * Brownian Motion.

*Lecture 36, April 22: * Brownian Motion.

*Lecture 37, April 24: * Brownian Motion.

*Lecture 38, April 29: * Brownian Bridge. Notes by Pitman [notes]

### Homework

Homeworks will be posted on Fridays and due in the following Fridays. The first will be assigned in week 2 and due in week 3.
**Week 3: ** Due February 6: PDF Solutions

**Week 4: ** Due February 13: PDF Solutions

**Week 5: ** Due February 20: PDF Solutions

**Week 6: ** No homework but here is a practice midterm PDF Solutions

**Week 7: ** Due March 6: PDF Solutions

**Week 8: ** Due March 13: PDF Solutions

**Week 9: ** Due March 20: PDF Solutions

**Week 10: ** Due April 3: PDF Solutions

**Week 12: ** Due April 17: PDF Solutions

**Week 13: ** Due April 24: PDF Solutions

**Week 14: ** Due May 1: PDF Solutions

### Section

Here are handouts and solutions for the weekly sections.
**Section 2: ** : Handout

**Section 3: ** Handout Solutions