DEPARTMENT OF MATHEMATICS
MTL 725 (
II Semester 2022-23
Lecture Classes (Slot M): Monday and Thursday between 5:00 PM and 6:20 PM
Pre-requisite: MTL 108 (Introduction to Statistics) or MTL 601 (Probability and Statistics)
INFORMATION SHEET
Course
contents
Stochastic processes, specification of stochastic processes, stationary processes, applications in engineering
(No. of Lectures - 4)
Renewal processes and theory, Markov renewal, semi-Markov processes, Markov regenerative processes, applications in communication systems
(No. of Lectures - 10)
Markov processes with continuous state space, martingales, applications in financial mathematics
(No. of Lectures - 14)
Markov chains, discrete time and continuous time Markov chains, branching processes, birth and death processes, applications in queueing systems
(No. of Lectures - 14)
Main Text Books
1.
Stochastic
Processes, J Medhi, 3rd edition, New Age International Publishers, 2009.
2.
Stochastic Processes, Video course, NPTEL Phase II.
3.
Stochastic Processes, Web course, NPTEL Phase II (with Prof. N. Selvaraju)
4.
A First Course in
Stochastic Processes,
Reference Books
2. Stochastic Processes, Sheldon M. Ross, 2nd
edition, John Wiley, 1995.
3. An
Introduction to Stochastic Modeling,
4. Introduction
to Stochastic Process, A K Basu, Narosa
Publishing House, 2003.
| Sl. No. | Topics | Videos | Relevant Tutorial Sheet |
| 1 | Stochastic processes, specification of stochastic processes, stationary processes, applications in engineering | Part 1, Part 2, Part 3, Part 4, Part 5 Part 6, Part 7, Part 8 | 1 |
| 2 | Discrete time Markov chains | Part 1, Part 2, Part 3, Part 4, Part 5, Part 6, Part 7, Part 8, Part 9, Part 10, Part 11, Part 12, Part 13, Part 14, Part 15, Part 16, Part 17, Part 18, Part 19, Part 20, Part 21, Part 22, Part 23, Part 24 | 2 |
| 3 | Continuous time Markov chains, birth and death processes, applications in queueing systems | Part 1, Part 2, Part 3, Part 4, Part 5, Part 6, Part 7, Part 8, Part 9, Part 10, Part 11, Part 12, Part 13, Part 14, Part 15, Part 16, Part 17, Part 18, Part 19, Part 20, Part 21, Part 22, Part 23, Part 24, Part 25, Part 26, Part 27, Part 28, Part 29 | 3 |
| 4 | Markov processes with continuous state space, martingales, applications in financial mathematics | To be included | 4 |
| 5 | Renewal processes and theory, Markov renewal, semi-Markov processes, Markov regenerative processes, applications in communication systems | Part 1, Part 2, Part 3, Part 4, Part 5, Part 6, Part 7, Part 8, Part 9, Part 10, Part 11, Part 12, Part 13, Part 14, Part 15, Part 16 | 5 |
| 6 | Branching processes | Part 1, Part 2, Part 3, Part 4, Part 5, Part 6 | 6 |
Note: The above classification of lecture notes are tentative only. (courtesy: NPTEL course)
(To be filled later)
Scheme of Evaluation
|
Two Minor Tests of 25 Marks each |
2X 25 |
50 |
|
One Major Examination |
1 X 50 |
50 |
|
|
Total |
100 |
IMPORTANT INFORMATION
·
Students are encouraged to contact the Course
Coordinator or Course Instructor for any difficulties regarding the course.
·
It is required that 75% attendance in lectures and
75% attendance in tutorials is a must in order to be eligible to appear in the
major examination.
·
One common make up examination will be conducted
towards the end of the semester. Only those students who could not appear for
one of the minor tests due to medical
reasons are eligible for the make up
examination. However, submission of a valid medical certificate adhering to the
institute norms is mandatory.
·
The evaluated minor answer books will be returned
to the students and they must retain with them as a proof of the marks secured.
INFORMATION about the Instructors
|
Name |
Room No. |
Phone No. |
Email |
|
|
MZ 164 |
7104 |
dharmar@maths.iitd.ac.in |