AIS Stochastic Processes (2018)

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Venue: National Institute of Science Education and Research,  Bhubaneswar, Odisha(Orissa)
Date:  25th, Jun 2018 to 21st, Jul 2018

 

School Convener(s)

Name Prof. Nabin Kumar Jana Prof. Rahul Roy
Mailing Address NISER, Bhubaneswar ISI, Delhi

 


 Speakers with their affiliations:

Sr. Speaker Affiliation
1 Anish Sarkar,(AS) ISI, Delhi
2 Antar Bandyapadhyay, (AB) ISI, Delhi
3 Arijit Chakrabarty,(AC) ISI, Kolkata
4 Krishanu Maulik, (KM) ISI, Kolkata
5 Nabin Kumar Jana, (NKJ) NISER, Bhubaneswar
6 Parthanil Roy, (PR) ISI, Bangalore
7 Rajat Subhra Hazra,(RSH) ISI, Kolkata
8 Rahul Roy,(RR) ISI, Delhi

 


 Syllabus:

Sr. Speaker Topics covered
1 Anish Sarkar
  • Discrete Markov chains with countable state space, Examples including 2-state chain, birth and death chain, renewal chain, Ehrenfest chain, card shufing, etc.Classifcaaon of states, recurrence and transience; absorbing states, irreducibility, decomposiaon of state space into irreducible classes, Examples.
  • Absorbing chains, absorpaon probabiliaes and mean absorpaon ame, fundamental matrix Staaonary distribuaons, limit theorems, posiave and null recurrence, reversible chains. Periodicity, limit theorems for aperiodic irreducible chains. Introducaon to MCMC.
2

Antar Bandyapadhyay

  • Measurable funcaons, basic properaes, sigma-felds generated by funcaons, integraaon of measurable funcaons, properaes of integrals, MCT, Fatou’s Lemma, DCT. Chebyshev’s, Holder’s and Minkowski’s inequaliaes. LLp spaces. Finite product of measurable spaces, construcaon of product measures, Fubinis theorem. Probability spaces, random variables and random vectors, expected value and its properaes.
3 Arijit Chakrabarty
  • Review of basic probability Theory, Random walks
4 Krishanu Maulik
  • Independence. Various modes of convergence and their relaaon. The Borel-Cantelli lemmas. Weak Law of large numbers for i.i.d. fnite mean case. Kolmogorov 0-1 law. Strong law of large numbers for i.i.d. case. Characterisac funcaons and its basic properaes, inversion formula, Levy’s conanuity theorem. Lindeberg CLT, CLT for i.i.d. fnite variance case, Lyapunov CLT.
5 Nabin Kumar Jana
  • Metric spaces, open/closed sets, sequences, compactness, completeness, conanuous funcaons and homeomorphisms, connectedness, product spaces, completeness of C[0, 1] and L p spaces
6 Parthanil Roy
  • Doing integraaon beyond Riemann theory, infnite tosses of a fair coin Fields, sigma-felds, measures, sigma-fnite/fnite/probability measures, properaes, statement of Caratheodory extension theorem (outline of idea, if ame permits). Monotone class theorem, Dynkin’s pi-lambda theorem. Radon measures on fnite-dimensional Borel sigma-feld, distribuaon funcaons,
    correspondence between probability measures on Borel sigma-feld and probability distribuaon funcaons.
7 Rajat Subhra Hazra
  • Analyac funcaons, Cauchy-Riemann equaaons, polynomials, exponenaal and trigonometric funcaons Contour integraaon, Power series representaaon of analyac funcaons, Liouville’s theorem, Cauchy integral formula, Cauchy’s theorem, Morera’s theorem, Cauchy-Goursat theorem Singulariaes, Laurent Series expansion, Cauchy residue formula, residue calculus. Meromorphic funcaons, Rouche’s theorem.
8 Rahul Roy
  • Random walk: Recurrence and transience, Generaang funcaon, convoluaon, fxed point of generaaon funcaon, convergence of p.g.f., Branching processes, Gambler’s Ruin problem, Arc Sine law
  • Three topics were covered during the four weeks of the course, viz., (i) analysis, (ii) Introductory stochastic processes and (iii) measure theoretic probability.
  • Notes were given by the instructors to the students.
  • The total contact hours per topic were as follows
    • Analysis -- 20 hours classroom teaching and 10 hours of tutorial
    • Stochastic processes -- 30 hours classroom teaching and 15 hours of tutorial
    • Measure theory -- 30 hours classroom teaching and 15 hours of tutorial
       

 Time Table

Week 1
09:00-11:00 11:30- 12:30 14:30-16:30 17:00-18:00
SP I
AC
Tutorial
AC & NKJ
Analysis I
NKJ
Tutorial
NKJ & AC
Week 2
Analysis II
RSH
Tutorial
RSH & PR
MTP I
PR
Tutorial
PR & RSH
Week 3
SP II
RR
Tutorial
RR & AB
MTP II
AB
Tutorial
AB & RR
Week 4
SP III
AS
Tutorial
AS & KM
MTP III
KM
Tutorial
KM & AS

 


List of Participants

SID Full Name Name of college/ University where employed/ studying Position in College/ University  
18711 Dr. Debashish Bose Shiv Nadar University Assistant Professor  
18680 Mr. Tejaswi Tripathi Indian Statistical Institute M.Math Student  
18869 Mr. Ramakrushna Mishra Department Of Statistics, Utkal University M.Sc. Student  
18964 Mr Vishal Subedi BIT Mesra IMSc Student  
19043 Mr. Anshul Kumar IIT ROORKEE PhD STUDENT  
19074 Ms. Kalai Selvi PSG College of Technology PhD Left the programme in the middle due to health reason.
19138 Mr. Soham Ghosh University Of Kalyani MSc Student  
19317 Mr. Mohammed Hisham M Pondicherry University Ph.D.  
19454 Ms. Aastha Shukla Hindu College (University of Delhi) MSc Student  
19501 Mr. Suvadip Sana Indian Statistical Institute,Bangalore. Undergrad (B. Math)  
19631 Ms. Sujata Goala DIBRUGARH UNIVERSITY M.Phill Scholar.  
19688 Mr. Anindya Ghatak NISER Phd student  
19689 Ms. Neha Gupta Indian Institute of Technology, Ropar PhD  
19704 Ms Divya Murali IIT Madras PhD Student  
19841 Mr. Tejinder Kumar Indian Institute of Technology Roorkee Department of Statistics and Center for Advanced PhD  
19890 Ms. Saranjeet Kaur Satnam Singh Bhogal Studies, Savitribai Phule Pune University (formerly University of Pune) MPhil Student  
19896 Mr. Arya Gangopadhyay University of Kalyani Integrated MSc Student  
19971 Miss Sejal Gopal Patil P.E.S.Modern college shivajinagar pune MSc student  
20006 Mr. Shivam Dhama Indian Institute of Technology PhD  
20047 Mr. Mashkoor Ali IIT ROORKEE Phd  
20071 Ms. Priyanka Sen ISI,KOLKATA PhD  
20098 Mr. Santosh Roy UNIVERSITY OF KALYANI Msc Student  
20203 Mr. Surya Narayan Maharana IIT Ropar Ph.D  
20242 Mr. B Sagar RAVENSHAW UNIVERSITY M.Sc Student  
20252 Mr. Himanshu Pokhriyal COCHIN UNIVERSITY OF SCIENCE AND TECHNOLOGY UM-DAE Centre for PhD  
20334 Mr. Charu Shardul Excellence in Basic Sciences Student  
20394 Ms. Ekta Punia IIT Gandhinagar PhD student   
20456 Mr. Ratul Biswas Indian Institute of Science Undergraduate  
20480 Mr. Albert Bansala Jawaharlal Nehru University MSc Student  
20493 Mr. Riyaz Gazi UNIVERSITY OF CALCUTTA MSc Student  
20506 Mr. Pritam Ghosh UNIVERSITY OF KALYANI MSc Student  
20568 Ms Medha Sunil Kale Department of Statistics, Savitribai Phule Pune MSc Student  
20590 Mr Hasan Bhagat University Amity University Kolkata Student  
20659 Mr. Dipankar Paul UNIVERSITY OF CALCUTTA MSC  
20676 Mr. Jewel Mahajan UNIVERSITY OF CALCUTTA (SCIENCE MSc Student  
20678 Mr Saikat Patra COLLEGE) UNIVERSITY OF CALCUTTA M.Sc Student  
20709 Mr. Akhil Kumar Sahoo Indian Institute of Science Education and Research, Kolkata MSc Student  
20714 Mr Dhirendra Kumar Central University of Integrated M.Sc  
20809 Mr. Parthasarathy Sai Telikicherla Rajasthan National Institute of Science Education and Research Student Msc Student  
20821 Mr. Pritam Laskar National Institute of Science, Education and Research (NISER) Msc Student  
20822 Ms. Mayuri Bakshi IIT Bombay MSc+PhD Student  
20830 Mr. Rushi Prasad Sahoo Utkal university PhD  
20841 Mr Abhinav Raj National Institute of Science Education and Research IntegratedStudent MSc  
20847 Ms. Pratiksha Bharat Shinde Tuljaram Chaturchand College of Arts, Science and Commerce. National Institute of MSc Student  
20923 Mr Deepak Kumar Science Education and Research Int.MSc. student  
18807 Mr. Barniit Adhikary UNIVERSITY OF KALYANI MSC STUDENT  
18881 Ms. Jita Parida College of Engineering Bhubaneswar , Lecturer Allowed since she was desperate to attend and some selected participants were absent
19528 Mr. Nitin Raja Singh Indian Institute of Technology, Delhi PhD Allowed since he was desperate to attend and some selected participants were absent

 

 


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