MTL 725 Stochastic Processes and Its Applications

DEPARTMENT OF MATHEMATICS

MTL 725/7725 (3-0-0) Stochastic Processes and Its Applications

II Semester 2025-26

Lecture Classes (Slot AD): Tuesday and Friday between 3:30 PM and 4:45 PM in LH 316

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.     Introduction to Stochastic Processes: Queues, Finance, and Credit Risk, S Dharmaraja, Springer, 2025.

2.     Stochastic Processes, J Medhi, 3^rd edition, New Age International Publishers, 2009.

3.     Stochastic Processes, Video course, NPTEL Phase II.

4.     Stochastic Processes, Web course, NPTEL Phase II (with Prof. N. Selvaraju)

5.     A First Course in Stochastic Processes, S Karlin and H M Taylor, Academic Press, 2^nd edition, 1975.

Reference Books

1.     Introduction to Probability and Stochastic Processes with Applications, Liliana Blanco Castaneda, Viswanathan Arunachalam, Selvamuthu Dharmaraja, Wiley, New Jersey, June 2012.

2.     Stochastic Processes, Sheldon M. Ross, 2^nd edition, John Wiley, 1995.

3.     An Introduction to Stochastic Modeling, S Karlin and H M Taylor, Elsevier, 1998.

4.     Introduction to Stochastic Process, A K Basu, Narosa Publishing House, 2003.

Lecture Notes
Introduction to this course

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)

Name	Room No.	Phone No.	Email
S Dharmaraja	615, Academic Complex West	7104	dharmar@maths.iitd.ac.in

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