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AIS Stochastic Processes - Level I

Monday, June 17, 2019 (All day) to Friday, July 12, 2019 (All day)
AIS - Stochastic Processes - level I

Most Indian Universities however do not have a rigorous study on probability. The aim of this school is to give a comprehensive training to students in a undergraduate/PhD programme onprobability and stochastic processes. Also to give them a chance to interact with researchers in these topics.
We propose to run three courses – 1) Basic probability theory, 2) Measure free Markov chain, 3)Modules of linear algebra and real analysis. There will be around 40 hours of lectures includingtutorials per topic over a 4 weeks period. In addition, over two weekends we plan to invite activeresearchers in probability to present introductory lectures on a research topic and interact withstudents.


a) Nabin Kumar Jana, Assistant Professor, NISER, Bhubaneswar

b) Rahul Roy, Professor, ISI, Delhi


Target audience: 3rd year of B.Sc.; 1st year of M.Sc. or 3rd & 4th year of Integrated M. Sc. students in Mathematics or Physics, 4th Year B.Tech. students in Electrical Engineering.


Speakers: Any 8 out of the following:
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) Probal Choudhuri, ISI, Kolkata

l) Alok Goswami, ISI, Kolkata


Syllabus: We plan to cover the following topics in this AIS.
Modules of Linear Algebra and Analysis:
     Linear Algebra: Vector Spaces: Denition 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, Matrix Representation of Vector Spaces, Bases, etc., Idempotent Matrices, Special Products of Matrices; Eigenvalues and Reduction of Matrices: Classication 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: Denitions, Separation Theorems for Convex Sets


     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
    Reference Texts:
    1. C.R. Rao: Linear Statistical Inference and Its Applications.
    2. A. Ramachandra Rao and P. Bhimasankaram: Linear Algebra.
    3. G. F. Simmons: Introduction to Topology and Modern Analysis
    4. J. C. Burkill and H. Burkill: A second course in mathematical Analysis

Basic Probability Theory:
   Orientation, Elementary concepts: experiments, outcomes, sample space, events. Discrete sample spaces and probability models. Combinatorial probability and urn models; Conditional probability and independence; Random variables { discrete and continuous; Expectations, variance and moments of random variables; Transformations of univariate random variables; Jointly distributed random variables; Conditional expectation; Generating functions; Limit theorems;

    Reference Texts:
    a) S. M. Ross: A rst course in Probability
    b) Jacod & Protter: Probability Essentials
    c) W Feller: An Introduction to Probability: Theory and Its Applications, Vol I & II
    d) George G. Roussas: Introduction to Probability


Markov Chain:
Random Walk, Discrete Markov chains with countable state space. Classication 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. Poisson process, continuous time markov chain with countable state space, continuous time birth and death chains.

  Reference Texts:
1. W. Feller: Introduction to the Theory of Probability and its Applications, Vol. 1.
2. P.G. Hoel, S.C. Port and C.J. Stone: Introduction to Stochastic Processes.
3. S.M. Ross: Stochastic Processes.
4. S. Karlin and J. Taylor: Stochastic Processes, Vol. 1.
5. J.G. Kemeny, J.L. Snell and A.W. Knapp: Finite Markov Chains.


Last date of application is 10th May 2019.


Application form is available here.


List of selected participants:



Name Confirmation of Participation
28170 Mr. Sadhanandh Vishwanath Confirmed
28199 Mr. Yogesh Kumar Confirmed
28270 Mr. Shivam Kumar Confirmed
28275 Ms. S Angel Auxzaline Mary No confirmation received
28290 Ms. Kanchana M Pending
28306 Mr Shyam Surykant Dhamapurkar No confirmation received
28309 Mr. Sanket Nemichand Teli Confirmed
28329 Mr Subhra Jyoti Nayak Confirmed
28333 Mr Bikram Mahapatra Confirmed
28352 Ms Sathya S Pending
28354 Ms Ashweta Padhan Confirmed
28356 Mrs Subhashini Marappan Pending
28365 Ms. Sonali Pradhan Confirmed
28368 Mr Brajamohan Sahoo Confirmed
28369 Ms. Sabhyata Rout Confirmed
28371 Mr. Ajay Shanmuga Sakthivasan Confirmed
28409 Mr. Krushna Chandra Sahoo No confirmation received
28447 Mr. Sachin Sachdeva Confirmed
28449 Ms. Subhashree Sahu No confirmation received
28456 Mr. Saptarshi Saha Confirmed
28464 Mr. Pallab Kumar Sinha Confirmed
28485 Ms. Km Sandhya Duplicate
28489 Mr Shantam Gulati Confirmed
28496 Mr Manas Jana Confirmed
28499 Mr Sougata Jana Confirmed
28534 Mr. Vivek Kumar Singh Confirmed
28560 Mr. Ravi Ashok Satpute Confirmed
28563 Ms. Km Sandhya Confirmed
28580 Mr Praneet Nandan Confirmed
28582 Mr. Hiranmay Das Confirmed


Second List:

SID Full Name Confirmation of participation
28123 Mr. Mayavel P Confirmed
28188 Mrs. Sangita Das Confirmed
28234 Mr Mostafizar Khandakar Selected for Level II
28328 Ms. Niharika Bhootna Confirmed
28336 Mr. Kunal Verma Confirmed
28508 Mr Vrikshavardhana Hebbar N Pending
28517 Ms. Debolena Basak Not confirmed
28572 Ms. Sarita Sarita Pending



  • To ensure the utilization of our full resources, selected participants through second list are requested to confirm their participation by 22nd May, 2019 to aissp @
  • To confirm the participation, a mail along with inwards travel documents, that is, copy of your train/bus tickets has to be send to aissp @ For local participants there is no need of any travel documents, only confirmation mail will suffice.
  • For those who will travel by train, the nearest railway station from NISER, Bhubaneswar is “Khurda Road”. So book your ticket accordingly.
  • Hostel accommodation from 16th June to 13th July 2019 will be provided to the participants but participants has to bring their own bedcover.
  • Food (breakfast, lunch & dinner) will be served from evening of 16th June to morning of 13th July 2019. Along with the confirmation, please let us know if you have any dietary restrictions.

  • Based on the reply, a Third list of selected candidates may be published on 23rd May 2019.







Contact us

School of Mathematical Sciences

NISERPO- Bhimpur-PadanpurVia- Jatni, District- Khurda, Odisha, India, PIN- 752050

Tel: +91-674-249-4081

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