Math 495 - Spring 2017

Stochastic Processes

Section Information

Section	Time	Location	Instructor	Office Hours (Cupples I, Room 17)
1	Mo-We 4:00 PM - 5:30 PM	Duncker 101	Renato Feres	Tu-Th 12:00 PM - 3:00 PM

Please include [Math495] in the subject line of any email message that pertains to this course. This will help avoid that I accidentally delete your message. My e-mail address is feres@math.wustl.edu.

Text

Introduction to Stochastic Processes, 2nd Edition, by Gregory F. Lawler
Chapman & Hall, 2006

Topics to be covered

This course is an introduction to stochastic processes. Topics to be covered are:

Finite Markov chains;
Countable Markov chains;
Continuous time Markov chains;
Optimal stopping;
Martingales;
Elements of MCMC
Brownian motion
Elements of stochastic differential equations

Mathematics software

This is mainly a "theory" course and computer work is not as central to it as for example in Statistics, Math 3200.
Homework assignments will, nevertheless, contain a mixture of questions, some more theoretical involving proofs or computations by hand, and a few involving computer work.

You may use any system for mathematics programming you wish (for example, Matlab, Mathematica, Maple, Python, etc.), but I recommend R because this is what I will use when writing solutions to the problem sets.

In the R computing main page you'll find instructions for downloading and installing R and general documentation. In particular, the manual An Introduction to R is a useful source of information.

Although the plain R program is nice enough in my opinion, there are free programs that provide more friendly user interface environments. For example, I like RStudio.

It is very likely that many of you have used R before, but I do not assume that you have. The information provided in the problem sets themselves and occasionally in class should be enough for the needs of the course even if you are using it for the first time.

Grading Information

I plan to have 10 weekly homework assignments, one midterm, and one final exam. The midterm exam will be in class, 80 minutes long, and will be based on content covered in the homework sets. The midterm exam date is 3/01/2017 (during class time, in Duncker 101) and the final exam is on 5/05/2017 from 6:00PM to 8:00PM (place to be announced). The worst homework score will be dropped. Midterm and final exams will each have twice the weight of a homework assignment.

Therefore the final score will be determined as follows: (1) linearly scale each homework or exam score for a maximum of 100 points; (2) then add the 9 best homework assignment scores plus twice the midterm exam score plus twice the final exam score and divide the total by 13.

The total score, out of 100, will be translated into a letter grade of A, B, C, D, F (with plus and minus shadings) in a way that is not harsher than indicated on the following table (if the grade distribution of the whole class is significantly lower than usual, then "curving" may be considered, but it is unlikely to be needed):

Numerical Range	Letter Grade
[85, 100]	A
[70, 85)	B
[60, 70)	C
[50, 60)	D
[0, 50)	F

Pluses and minuses are assigned so that each letter range is divided in three populations of roughly equal size. So, for example, the number of students getting A-, A, A+ will be approximately the same. Please note: this does not mean that A- corresponds to the interval [85, 90) or that A corresponds to [90, 95)! In particular, the exact grade cut-offs for the signs will not be known, to you as well as to me, until after the final exam.

Homework

The plan is to have a total of 10 HW assignments. Of these, the 9 best scores will count towards the total.

Weekly assignments deadline is Friday 5:00PM. You should submit them using Crowdmark. (I'll have more to say about it on the first day of class.)

Under exceptional circumstances, I may accept them at a different time on Friday, but I plan on posting solutions on Saturday. Late assignment will not be accepted after solutions are posted.

You are both allowed and encouraged to collaborate on your assignments.

Course plan

Please keep in mind that the plan given below is tentative. We may fall behind (likely) or ahead (less likely) of the planned schedule on any given week.

Week	Textbook section covered
Jan 18 - Jan 20 Homework 0 (not for grade; won't be collected)	0.1, 0.2, 0.3
Jan 23 - Jan 27 Homework 1: 1/27 Solutions	1.1, 1.2, 1.3, 1.4
Jan 30 - Feb 03 Homework 2: 2/04 Solutions	1.4, 1.5, 1.6
Feb 06 - Feb 10 Homework 3: 2/11 Solutions	2.1, 2.2, 2.3, 2.4
Feb 13 - Feb 17 Homework 4: 2/18 Solutions	3.1, 3.2, 3.3, 3.4
Feb 20 - Feb 24 Homework 5: 2/25 Solutions	3.4, 4.1, 4.2, 4.3
Feb 27 - Mar 03 Midterm: 3/01 Solutions	5.1, 5.2, 5.3
Mar 06 - Mar 10 Homework 6: 3/11 Solutions	5.4, 5.5, 5.6
Mar 20 - Mar 24	7.1, 7.2, 7.3
Mar 27 - Mar 31 Homework 7: 4/01 Solutions	7.3, 7.4, 8.1, 8.2
Apr 03 - Apr 07	8.3, 8.4, 8.5
Apr 10 - Apr 14 Homework 8: 4/15 Solutions	8.6, 8.7, 8.8, 9.1, 9.2
Apr 17 - Apr 21 Homework 9: 4/22 Solutions	9.3, 9.4
Apr 24 - Apr 28 Homework 10: 4/29 Solutions	9.5, 9.6, 9.7
May 05 - Final Exam Final: 5/05 (6:00PM - 8:00PM, place to be announced) Solutions

Renato Feres
feres@math.wustl.edu
Cupples I, Room 17
(314) 935 - 6752 (office phone)

Department of Mathematics
Washington University
Campus Box 1146
Saint Louis
Missouri, 63130 USA.

Last Updated: January 11, 2017