AIS - Stochastic Processes and Applications (2024)
Speakers and Syllabus
Syllabus: (Each speaker is required to deliver minimum 6 lectures).
|
Name of the Speaker with affiliation |
No. of Lectures |
Detailed Syllabus |
|
Prof. Parthanil Roy ISI Bangalore |
7.5 hrs |
Definition and examples of Discrete-time Markov chains, 1 and n-step transition probability matrices; Communication and irreducibility; Hitting times and absorption probabilities; Strong Markov Property; Recurrence and transience; Invariant distributions. limit theorems for discrete-time Markov chains. |
|
Dr. Subhamay Saha IIT Guwahati |
6 hrs |
Reversible Markov chains Definition and properties of Renewal Processes; Renewal equations and its generalizations; Elementary renewal theorem, Key renewal theorem; Excess life and age distribution; Renewal reward processes. |
|
Dr. Koushik Saha IIT Bombay
|
6 hrs |
Exponential distribution and its properties; Definition of Poisson processes, Inter-arrival times, nth arrival time, conditional arrival times; Poisson thinning, merging of two independent Poisson processes; Compound Poisson processes. |
|
Dr. Chandan Pal IIT Guwahati |
4.5 hrs |
Definition and examples of continuous-time Markov chains; Rate matrix, transition probability function, Kolmogorov forward and backward equations; Birth-death processes; Limiting probabilities. |
|
Prof. Mrinal K. Ghosh IACS, Kolkata |
6 hrs |
Discrete-time Markov decision processes; Finite horizon problems; Infinite horizon discounted and average cost problems. Semi-Markov decision processes; Infinite horizon discounted and average cost problems. |
|
Prof. N. Selvaraju IIT Guwahati |
6 hrs |
Characteristics of queueing systems, Little’s law, Markovian and non-Markovian queueing systems, embedded Markov chain applications to M/G/1, G/M/1 and related queueing systems; Networks of queues, open and closed queueing networks; Queues with vacations, priority queues. |
References:
- J. R. Norris, Markov Chains, Cambridge University Press, 1997.
- S. M. Ross, Stochastic Processes, 2nd edition, Wiley, 2008.
- S. M. Ross, Applied Probability Models with Optimization Applications, Dover Publications, 1992.
- D. Gross and C. Harris, Introduction to Queueing Theory, 3rd Edition, Wiley, 1998 (WSE Edition), 2004.
Tutorial Assistants:
|
S. No. |
Name |
Affiliation |
|
1 |
Bivakar Bose |
IIT Guwahati |
|
2 |
Amit Ghosh |
IIT Guwahati |
|
3 |
Pratim Dey |
IIT Guwahati |
Time Table
Time-Table (with names of speakers and course associates/tutors):
|
Day |
Date |
Lecture 1 (9.30–11.00) |
Tea (11.05 To |
Lecture 2 (11.30 |
Lunch (1.05 |
Tutorial (2.30 |
Tea (3.35 to |
Tutorial (4.00 |
Snacks 5.05 to |
|
|
|
(name of the speaker) |
|
(name of the speaker) |
|
(name of the speaker + tutors) |
|
(name of the speaker + tutors) |
|
|
Mon |
13/5 |
DTMC-1(PR) |
|
DTMC-2(PR) |
|
PR+PD+AG |
|
PR+PD+AG |
|
|
Tues |
14/5 |
PP-1(KS) |
|
DTMC-3(PR) |
|
KS+PD+AG |
|
PR+PD+AG |
|
|
Wed |
15/5 |
DTMC-4(PR) |
|
PP-2(KS) |
|
PR+PD+BB |
|
KS+BB+AG |
|
|
Thu |
16/5 |
DTMC-5(PR) |
|
PP-3(KS) |
|
PR+BB+AG |
|
KS+BB+PD |
|
|
Fri |
17/5 |
DTMC-6(SS) |
|
PP-4(KS) |
|
SS+BB+AG |
|
KS+PD+BB |
|
|
Sat |
18/5 |
RP-1(SS) |
|
CTMC-1(CP) |
|
SS+PD+AG |
|
CP+BB+AG |
|
|
SUNDAY: OFF |
|||||||||
|
Mon |
20/5 |
RP-2(SS) |
|
CTMC-2(CP) |
|
SS+AG+BB |
|
CP+BB+PD |
|
|
Tues |
21/5 |
RP-3(SS) |
|
CTMC-3(CP) |
|
SS+BB+PD |
|
CP+BB+AG |
|
|
Wed |
22/5 |
MDP-1(MKG) |
|
QT-1(NS) |
|
MKG+PD+AG |
|
NS+PD+BB |
|
|
Thu |
23/5 |
MDP-2(MKG) |
|
QT-2(NS) |
|
MKG+PD+AG |
|
NS+AG+BB |
|
|
Fri |
24/5 |
MDP-3(MKG) |
|
QT-3(NS) |
|
MKG+PD+AG |
|
NS+PD+BB |
|
|
Sat |
25/5 |
MDP-4(MKG) |
|
QT-4(NS) |
|
MKG+BB+PD |
|
NS+AG+BB |
|
DTMC- Discrete-time Markov Chains
PP- Poisson Processes
RP- Renewal Processes
CTMC- Continuous-time Markov Chains
MDP- Markov Decision Processes
QT- Queueing Theory
Full forms for the abbreviations of speakers and tutors:
PR: Parthanil Roy
KS: Koushik Saha
SS: Subhamay Saha
CP: Chandan Pal
MKG: Mrinal K. Ghosh
NS: N Selvaraju
PD: Pratim Dey
AG: Amit Ghosh
BB: Bivakar Bose