Instructor: Antar Bandyopadhyay (Email: antar (at) isid (dot) ac (dot) in Office: 208 Faculty Building).

Class Time: Mon Thu 14:00 - 15:30 in Class Room 23 (on first floor).

Instructor's Office Hours: Mon Thu 11:30 - 13:00

Course Duration: September 7 - December 11, 2009.

Midterm Examination: October 26, 2009 (Monday)

Final Examination: December 21, 2009 (Monday)

Course Outline:

• Classical branching processes, generating function techniques, limit theorems.
• Multi-type branching processes.
• One dimensional continuous time Markov branching processes.
• Applications in study of discrete probability models.

References:

• For General Branching Processes:
  • Branching Processes by K. B. Athreya and P. E. Ney.
  • Branching Processes by S. Asmussen and H. Hering.
  • The Theory of Branching Processes by T. E. Harris.
  • Multitype Branching Processes by C. J. Mode.

• For Application of Branching Processes:
  • Random Graphs by S. Janson, T. Luczak and A. Rucinski.
  • Percolation by G. Grimmett.
  • Stochastic Interacting Systems:Contant, Voter and Exclusion Processes by T. M. Liggett.
  • Probability on Trees by R. Lyons and Y. Peres
    (available at http://mypage.iu.edu/~rdlyons/prbtree/prbtree.html).

Prerequisites:

• Real Analysis (at the level of Principles of Mathematical Analysis, W. Rudin).
• Liner Algebra (at the level of Finite Dimensional Vector Spaces, P. R. Halmos).
• Measure Theoretic Probability (at the level of Probability and Measure, P. Billingsley).
• Theory of Discrete Parameter Martingale (at the level of Probability and Measure, P. Billingsley).

Grading Policy:

• Assignments: 40% of the total credit.
• Midterm Exam: 20% of the total credit.
• Final Exam: 40% of the total credit.

Assignment Policies:

• There will be a total of 13 sets of homework assignments each carrying a total of 20 points. 10 best assignment scores will be taken for the final grading.
• Except for the midterm week, assignments will be given in class on every Monday, and it will be due in class on Monday of the following week. Each assignment set will be based on course materials covered in the lectures in the week before it is assigned. For example, the assignment given on September 14 (Monday) will be due on September 21 (Monday), and will be on materials covered in lectures on September 7 and 10.
• Late submission of an assignment will not be accepted. If you can not submit an assignment on time, don't worry about it, and try to do well in the others. It will not count in your final grade since you have few extra assignments anyway.
• Graded assignments will be returned in the class on the next Thursday following the due date. For example, the assignment which is due on September 21 (Monday) will be returned after grading on September 24 (Thursday).
• Click here for downloading the assignments.

Exam Policies:

• Each examination will be an open note examination. That means, students are allowed to bring his/her own hand written notes, study materials, list of theorems etc.
• No printed or photo copied materials are allowed in any examinations. In particular no books.

Last modified September 16, 2009.