Introduction to Stochastic Processes: Math 597/697

Meeting : MWF 11:15    LGRC A205

Instructor : Luc Rey-Bellet

 Office :  1423 J LGRT
 Phone :  545-6020
 E-Mail :  lr7q@math.umass.edu
 Office Hours :   Monday 1:30--3:00,   Wednesday 1:30--3:00,   or by appointment.

Text: Introduction to Probability Models, 8-th Edition, by Sheldon M. Ross, Academic Press.

Further references:

• Introduction to stochastic processes, by Gregory F. Lawler, Chapman&Hall.
• Stochastic Processes, by Sheldon M. Ross, Wiley.
• Adventures in Stochastic processes, by Sidney I. Resnick, Birkhauser.
• A first course in Stochastic Processes, by Samuel Karlin and Howard M. Taylor, Academic Press.
• Lectures on Contemporary probability, by Gregory F. Lawler and Lester N. Coyle, Student Mathematical Library, AMS.

Syllabus: This course is nonmeasure theoretic introduction to stochastic processes. As such it assumes only a knowledge of calculus and elementary probability. We emphasize examples and applications from various disciplines. Goals of the the course are to present some general aspects of the theory and to develop probabilistic thinking and intuition.

• 1) Conditional probability and conditional expectations.

• 2) Markov chains. Definition and basic properties, classification of states (recurrence and transience), stationary distribution and limit theorems, applications and examples.

• 3) Poisson processes.

• 4) Continuous-Time Markov chains, Birth and death processes, Kolmogorov equations, limit theorems, Queueing theory.

• 5) Brownian motion and applications

Grade :

• 40% Midterm
• 40% Final Exam
• 20% Homework, attendance and participation

Exams:

• Exam1:     MIDTERM PDF file
  
  
• Final:         Thursday 12/18 12:00--3:00         Room:         LGRC A205         The final is comprehensive. Closed notes, closed books.
  
  

Homework :

Homework #1 (due on Wednesday 09/17):   HW#1 PDF file      

Homework #2 (due on Wednesday 10/01):   HW#2 PDF file      

Homework #3 (due on Friday 10/17):           HW#3 PDF file      

Homework #4 (due on Wednesday 11/12):   HW#4 PDF file      

Homework #5 (due on Wednesday 12/03):   HW#5 PDF file      

Homework #6 (due on Friday 12/12):           HW#6 PDF file