AIS  Stochastic Processes  level I (2019)
Speakers and Syllabus
Syllabus: (Each speaker is required to deliver minimum 6 lectures).
Name of the Speaker with affiliation 
No. of Lectures 
Detailed Syllabus 
Teacher 1 
5 
Basic Probability Theory I: Orientation, Elementary concepts: experiments, outcomes, sample space, events. Discrete sample spaces and probability models. Combinatorial probability and urn models; Conditionalprobability and independence; 
Teacher 2 
5 
Linear Algebra: Vector Spaces: Definition of Vector Spaces and Subspaces, Basis of a Vector Space, Linear Equations, Vector Spaces with an Inner Product Theory of Matrices and Determinants: Matrix Operations, Elementary Matrices and Diagonal Reduction of a Matrix, Determinants, Transformations, Generalized Inverse of a Matrix, MatrixRepresentation of Vector Spaces, Bases, etc., Idempotent Matrices, Special Products of Matrices Eigenvalues and Reduction of Matrices: Classification and Transformation of Quadratic Forms, Roots of Determinantal Equations, Canonical Reduction of Matrices, Projection Operator,Further Results on gInverse, Restricted Eigenvalue Problem Convex Sets in Vector Spaces: Definitions, Separation Theorems for Convex Sets 
Teacher 3 
5 
Markov Chain I: Random Walk, Discrete Markov chains with countable state space. 
Teacher 4 
5 
Real Analysis: Metric spaces, open/closed sets, CauchySchwarz Inequality, Holder’s Inequality, Hadamard’s Inequality, Inequalities Involving Moments, Convex Functions and Jensen’s Inequality, Inequalities in Information Theory, Stirling’s Approximation sequences, compactness,completeness, continuous functions and homeomorphisms, connectedness, product spaces, completeness of C[0, 1] and Lp spaces, ArzelaAscoli theorem 
Teacher 5  5  Basic Probability Theory II: Random variables – discrete and continuous; Expectations, variance and moments of random variables; Transformations of univariate random variables; 
Teacher 6 
5 
Markov Chain II: Classification of states  recurrence, transience, periodicity. Stationary distributions, limit theorems, positive and null recurrence, ratio limit theorem, reversible chains. Several illustrations including the Gambler’s ruin problem, queuing chains, birth and death chains etc. 
Teacher 7 
5 
Basic Probability Theory III: Jointlydistributed random variables; Conditional expectation; Generating functions; Limit theorems; 
Teacher 8 
5 
Markov Chain III: Poisson process, continuous time markov chain with countable state space, continuous time birth and death chains. 
References:
1. A. Ramachandra Rao and P. Bhimasankaram: Linear Algebra.
2. G. F. Simmons: Introduction to Topology and Modern Analysis
3. S. M. Ross: A first course in Probability
4. Jacod & Protter: Probability Essentials
5. W. Feller: Introduction to the Theory of Probability and its Applications, Vol. 1.
6. P.G. Hoel, S.C. Port and C.J. Stone: Introduction to Stochastic Processes.
Time Table
TimeTable (with names of speakers and course associates/tutors):
Day 
Date 
Lecture 1 (9.00–11.00) 
Tea (11.05–11.25) 
Tutorial (11.30–12.30) 
Lunch (12.30–2.25) 
Lecture 2 (2.30–4.30) 
Tea (4.354.55) 
Tutorial (5.006.00) 
Snacks 6.056.30 



Speaker 

Speaker + Tutors 
Speaker 

Speaker + Tutors 


Mon 
17/06 
Teacher 1 

Teacher 1&2 

Teacher 2 

Teacher 1&2 


Tues 
18/6 
Teacher 1 

Teacher 1&2 

Teacher 2 

Teacher 1&2 


Wed 
19/6 
Teacher 1 

Teacher 1&2 

Teacher 2 

Teacher 1&2 


Thu 
20/6 
Teacher 1 

Teacher 1&2 

Teacher 2 

Teacher 1&2 


Fri 
21/6 
Teacher 1 

Teacher 1&2 

Teacher 2 

Teacher 1&2 


Sat 
22/6 
Tutorial 

Tutorial 

Tutorial 

Tutorial 


SUNDAY : OFF 

Mon 
24/6 
Teacher 3 

Teacher 3 & Biltu Dan 

Teacher 4 

Teacher 4 & Sukrit 


Tues 
25/6 
Teacher 3 

Teacher 3 & Biltu Dan 

Teacher 4 

Teacher 4 & Sukrit 


Wed 
26/6 
Teacher 3 

Teacher 3 & Biltu Dan 

Teacher 4 

Teacher 4 & Sukrit 


Thu 
27/6 
Teacher 3 

Teacher 3 & Biltu Dan 

Teacher 4 

Teacher 4 & Sukrit 


Fri 
28/6 
Teacher 3 

Teacher 3 & Biltu Dan 

Teacher 4 

Teacher 4 & Sukrit 


Sat 
Tour 

SUNDAY : OFF 

Mon 
01/7 
Teacher 5 

Teacher 5 & Biltu Dan 

Teacher 6 

Teacher 6 & Sukrit 


Tues 
02/7 
Teacher 5 

Teacher 5 & Biltu Dan 

Teacher 6 

Teacher 6 & Sukrit 


Wed 
03/7 
Teacher 5 

Teacher 5 & Biltu Dan 

Teacher 6 

Teacher 6 & Sukrit 


Thu 
04/7 
Teacher 5 

Teacher 5 & Biltu Dan 

Teacher 6 

Teacher 6 & Sukrit 


Fri 
05/7 
Teacher 5 

Teacher 5 & Biltu Dan 

Teacher 6 

Teacher 6 & Sukrit 


Sat 
06/7 
Tutorial 

Tutorial 

Tutorial 

Tutorial 


SUNDAY : OFF 

Mon 
08/7 
Teacher 7 

Teacher 7 & Biltu Dan 

Teacher 8 

Teacher 8 & Sukrit 


Tues 
09/7 
Teacher 7 

Teacher 7 & Biltu Dan 

Teacher 8 

Teacher 8 & Sukrit 


Wed 
10/7 
Teacher 7 

Teacher 7 & Biltu Dan 

Teacher 8 

Teacher 8 & Sukrit 


Thu 
11/7 
Teacher 7 

Teacher 7 & Biltu Dan 

Teacher 8 

Teacher 8 & Sukrit 


Fri 
12/7 
Teacher 7 

Teacher 7 & Biltu Dan 

Teacher 8 

Teacher 8 & Sukrit 

Speakers: Any EIGHT of the following according to their availability and mutual understanding
a) B V Rao, CMI, Chennai
b) Rahul Roy, ISI, Delhi
c) Anish Sarkar, ISI, Delhi
d) Antar Bandyapadhyay, ISI, Delhi
e) Krishanu Maulik, ISI, Kolkata
f) Parthanil Roy, ISI, Bangalore
g) Arijit Chakrabarty, ISI, Kolkata
h) Srikanth Iyar, IISc, Bangalore
i) Nabin Kumar Jana, NISER, Bhubaneswar
j) Manjunath Krishnapur, IISc, Bangalore
k) Alok Goswami, ISI, Kolkata
l) Probal Choudhuri, ISI, Kolkata
Tutorial Assistants:
S. No. 
Name 
Affiliation 
1 
Biltu Dan 
ISI, Kolkata 
2 
SukritChakraborty 
ISI, KOlkata 