Department of Mathematics, Spring 2005

Math 5652: Introduction to
Stochastic Processes

TuTh 4:40-6:35, 6 Vincent Hall

Instructor: Lea Popovic

Office Hours: TuTh 3:30-4:30 (or by appointment), 254 Lind Hall

Course Outline

The course will cover basic topics on stochastic processes introducing the most important concepts and illustrating their application with examples. Topics include:
  • Markov chains: definitions, classification, limit behaviour
  • Martingales: conditional expectations, optional stopping theorem
  • Poisson processes: properties, compound Poisson processes
  • Continuous Time Markov Chains: transition probabilities, limiting behaviour
  • Renewal Theory: laws of large numbers
  • Brownian Motion: random walks, properties, application to option pricing


Semester of Probability Theory, such as Math 5651 or Stat 5101.


"Essential Stochastic Processes" by R.Durrett, Springer, available at the Math library for a two hour loan.
(For more examples/exercises see: "One Thousand Exercises in Probability" by G.R. Grimmett and D.R. Stirzaker, Oxford)


  • Homework 40% - approximately 6-7 homework sets
  • Two mid-terms 30% each - in class exams, dates: March 24, May 3 or 10
There will be no make-up times for the mid-terms. If a serious reason prevents you from attending any of the mid-terms, you need to consult with me before the date of the exam.
Homeworks are due approximately a week after they have been handed out (exact dates are on the Homeworks site). Hand in your homeworks in class. Late homeworks can not be accepted. One lowest homework score can be dropped from the homework grade average.

Practice Exams 1   Note: expect more difficult problems   Practice Exam 1 Answers   Note: you will be expected to provide more detailed answers

Practice Exam 2   Note: expect to be asked to define terms   Practice Exam 2 Answer   Note: you should provide as detailed as possible answers


Grade Record
  • HmWk 1: max= 40,  ave= 29.2,  q1= 24,  q3= 33
  • HmWk 2: max= 55,  ave= 32.6,  q1= 23,  q3= 40
  • HmWk 3: max= 50,  ave= 36.5,  q1= 31,  q3= 46
  • HmWk 4: max= 40,  ave= 33.8,  q1= 31,  q3= 40
  • HmWk 5: max= 40,  ave= 23.9,  q1= 20,  q3= 29
  • Exam 1: max=100,  ave= 55.0,  q1= 39,  q3= 72

Lecture Schedule - there will be no class on Apr 21!