Introduction to Stochastic Processes: Math 597/697

Meeting : MW 8:40--9:55    LGRT 319

Instructor : Luc Rey-Bellet

 Office :  1423 J LGRT
 Phone :  545-6020
 E-Mail :  luc@math.umass.edu
 Office Hours :   Monday 10:30--12:00,   Wednesday 10:30--12:00,   or by appointment.

Text: Introduction to Stochastic Processes, by Gregory F. Lawler, Chapman&Hall.

Further references:

• Introduction to Probability Models, 8-th Edition, by Sheldon M. Ross, Academic Press
• Introduction to Stochastic Processes, by Paul G. Hoel, Sidney C. Port and Charles J. Stone, Waveland Press.
• 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.
• An introduction to Markov processes. by Daniel W. Stroock, Graduate Texts in Mathematics, Springer.
• Lectures on Contemporary probability, by Gregory F. Lawler and Lester N. Coyle, Student Mathematical Library, AMS.

Syllabus: This course is an introduction to stochastic processes. Prerequisite are a good knowledge of calculus and elementary probability as in Stat 515 or Stat 607. The two main goals of the course are to present some general concepts and techqniues of the theory of stochastic process and to develop probabilistic thinking and intuition. We emphasize examples and applications from various disciplines. Among the topics treated in the class are

• 1) Markov chains on discrete state spaces (both finite and countable). Definition and basic properties, classification of states (positive recurrence, recurrence and transience), stationary distribution and limit theorems, analysis of transient behavior, applications and examples.

• 2) Continuous-Time Markov chains. Definition and basic properties. Poisson Process, Birth and Death Process, Queueing models.

• 3) Reversible Markov processes and Monte-Carlo Markov algorithms.

• 4) Brownian motion and applications.

Grade :

• 40% Midterm (Take-home)
• 40% Final Exam
• 20% Homework, attendance and participation

Exams:

• Midterm:     Midterm PDF file
  
  
• Final:     Final PDF file

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  Homework :
  
  Homework #1 (due on February 15):   HW#1 PDF file       SOL#1 PDF file
  
  Homework #2 (due on February 27 ):   HW#2 PDF file       SOL#2 PDF file
  
  Homework #3 (due on March 10):   HW#3 PDF file       SOL#3 PDF file
  
  Homework #4 (due on March 29):   HW#4 PDF file       SOL#4 PDF file
  
  Homework #5 (due on April 19):   HW#5 PDF file            
  
  Homework #6 (due on April 26):   HW#6 PDF file      
  
  Homework #7 (due on May 17 ):   HW#7 PDF file      
  

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