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Robert T. Buche, MA/ST 747, Spring 2008

Lectures: T-H, HA 273, 10:15 - 11:30.

Office Hours: New: Remaining office hours:

  • Friday April 18, 10-11:30 AM.
  • Monday April 21, 1:00 PM - 2:30 PM.
  • Wednesday April 23, 1:00 - 2:00 PM
  • (Homework and Final exam pick-up or emailed) Monday April 28, Noon - 2:00 PM
  • Wednesday April 30, Noon - 1:30 PM

Syllabus, here

Key Announcements:

  • The Final exam will be handed out the first day of finals: Pick up of the final is Monday April 28, between Noon and 2:00 at my office (HA 150).
    • Projects are to be handed in with the final.
    • Due date for the final and projects: 11 AM, Monday May 5. Turn in at my office (HA 150).
  • Updated with some more hints: HW 6 (due Tues., April 22.)
  • Updated with a hint: HW 7 (short) (due Thursday, April 24.)

Homework Assignments:

  • Homework 1, here. Hints, here. Solutions here

  • Homework 2, here. Solutions, here.
  • Homework 3, here. (02/23) Updated with hints and a correction. Solutions, here
  • Homework 4, here . Solutions, (03-16, slight correction end #4) here
  • Homework 5, here . Solutions, here
  • Midterm, here. Solutions, here.
  • Homework 6, here. Solutions, here.
  • Homework 7, here. Solutions, here

 

 

Lecture Previews (outline):

  • 01/10: General discussion of syllabus topics.
  • 01/15: Review of probability spaces, random variables.
  • 01/17: R.v. (con't.) and expectation.
  • 01/22: Expected value and properties
  • 01/24: Conditional expectation: general development, without resort to geometrical results
  • 01/29: Conditional expectation: geometric development (applying functional analysis results)
  • 01/31: Conditional expectation : properties, some comments on joint distributions, some examples.
  • 02/05: Joint distributions. (Sub)-(super)-martingales: definitions and several examples and properties.
  • 02/07: Continue examples. Stopping times, Martingale convergence theorem.
  • 02/12: Martingale Convergence theorems Doob decomposition
  • 02/14: Examples using Mart. Convg. and Doob decomposition, Doob's inequality
  • 02/19: Doob Lp ininequality, Convergence theorems: a.s. and Lp. Uniform integrability
  • 02/21: Uniform integrability, convergence a.s., and in L1.
  • 02/26: Continue convergence result from 02/21 for submartingales and martingales, some examples. Levy 0-1 law.
  • 02/28-03.20: Komogorov 0-1, Dominated convergence for cond. expectation, Optional stopping theorems, backwards martingales.
  • 03/25: Markov chain introduction, construction of Markov chains and Kolmogorov extension, some examples.
  • 03/27: Formlization of MC described by transition probabilities. MC examples.
  • 04/01: MC examples, Markov property, chapman -kolmogorov.
  • 04/03: Strong Markov Property, reflection principle, example for SMP.
  • 04/08: SMP example, first passage decomposition example, recurrence and transience.

Special Notes:

  1. None yet.

 
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