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 g-Inverse, 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, Cauchy-Schwarz 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, Arzela-Ascoli 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

Time-Table (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

(4.35-4.55)

Tutorial

(5.00-6.00)

Snacks

6.05-6.30

 

 

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

 

 

 

 

 

 

 

 

 

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