Stochastic Processes (2023)

Convener(s)

 
Name: Dr. Nabin Kumar Jana Dr. Arijit Chakrabarty
Mailing Address: Reader-F
School of Mathematical Sciences
National Institute of Science Education and Research, Bhubaneswar
P.O. Jatni, Khurda, Odisha, 752050

Associate Professor
Theoretical Statistics and Mathematics Unit Indian Statistical Institute
203 B.T. Road,
Kolkata 700108
Email: nabinjana at gmail.com arijit.isi at gmail.com

Probability theory is now considered an integral part of mathematics. The mathematics programmes of most Indian Universities, however, do not include probability theory in much detail. The aim of this school is to give a comprehensive training in probability and stochastic processes to students of the undergraduate and postgraduate programmes. Besides, giving them a chance to interact with researchers in these topics is also a goal of this instructional school.

Dates: 

Monday, June 26, 2023 - 09:00 to Saturday, July 15, 2023 - 18:00

Venue: 

Venue Address: 

National Institute of Science Education and Research Bhubaneswar
P.O. Jatni, Khurda 752050, Odisha, India

 

 

Venue State: 

Venue City: 

PIN: 

752050

Syllabus: 

 


Name of the Speaker with affiliation

No. of Lectures

Detailed Syllabus
Suprio Bhar,
IIT, Kanpur		 10

Measure theoretic Probability I: Caratheodory extension theorem , Monotone class theorem, Dynkin’s pi-lambda theorem, MCT, Fatou’s Lemma, DCT, Fubini’s theorem. Probability spaces, random variables and random vectors, expected value and its properties.

Anish Sarkar

ISI, Delhi

10

Measure theoretic Probability II: Independence. Various modes of convergence and their relation. The Borel-Cantelli lemmas. Weak Law of large numbers for i.i.d. finite mean case. Kolmogorov 0-1 law, Kolmogorov’s maximal inequality. Statement of Kolmogorov’s three-Series theorem (proof if time permits). Strong law of large numbers for i.i.d. case. Characteristic functions and its basic properties, inversion formula, Levy’s continuity theorem. Lindeberg CLT, CLT for i.i.d. finite variance case, Lyapunov CLT.

Manjunath Krishnapur

IISc, Bengaluru

10

Conditional probability and martingales I: Absolute continuity and singularity of measures. Hahn-Jordon decomposition, Radon-Nikodym Theorem, Lebesgue decomposition. Conditional expectation – Definition and Properties. Regular conditional probability, proper RCP. Regular conditional distribution.

Soumendu Sudar Mukherjee

ISI, Kolkata

10

 Brownian Motion I: Introduction to Brownian Motion, Kolmogorov Consistency theorem, Kolmogorov Continuity theorem, Construction of BM. Basic Martingale Properties and path properties – including Holder continuity and non-differentiability.

Arup Bose

ISI, Kolkata

 10

Conditional probability and martingales II: Discrete parameter martingales, sub-and super-martingales. Doob’s Maximal Inequality, Upcrossing inequality, martingale convergence theorem, Lp inequality, uniformly integrable martingales, reverse martingales, Levy’s upward and downward theorems. Stopping times, Doob’s optional sampling theorem. Discrete martingale transform, Doob’s Decomposition Theorem. Applications of martingale theory: SLLN for i.i.d. random variables.
Alok Goswami

IACS, Kolkata

 10 Brownian Motion II: Quadratic variation. Markov Property and strong Markov property of BM, reflection principle, Blumenthal’s 0-1 law. Distributions of first passage time and of running maximum of BM.

References:
    1. Probability and Measure Theory: Robert B. Ash and Catherine A. Doleans-Dade
    2. A Course in Probability Theory: Kai Lai Chung.
    3. Probability and Measure: Patrick Billingsley
    4. Probability Theory: Leo Breiman
    5. Brownian motion: P. Morters and Y. Peres

(Lecture notes from the speakers, if available)

Time Table: 

Time-Table
(with names of speakers and course associates/tutors)

Day

Date

Lec 1&2
9.00
to
11.00

Tea
11.05
to
11.25

Tut
11.30
to
12.30

Lunch
12.30
to
2.25

Lect 3&4
2.30
to
4.30

Tea
4.35
to
4.55

Tut
5.00
to
6.00

Snacks
6.05
to
6.30

 

 

(name of the speaker)

 

(name of the speaker + tutors)

 

(name of the speaker)

 

(name of the speaker + tutors)

 

Mon

Week

1

SB

 

SB & SC

 

AS

 

AS & PS

 

Tues

SB

 

SB  & SC

 

AS

 

AS & PS

 

Wed

SB

 

SB & SC

 

AS

 

AS & PS

 

Thu

SB

 

SB & SC

 

AS

 

AS & PS

 

Fri

 

SB

 

SB & SC

 

AS

 

AS & PS

 

Sat

Tutorial
(NKJ, SC, PS)

 

Tutorial
(NKJ, SC, PS)

 

Tutorial
(NKJ, SC, PS)

 

Tutorial
(NKJ, SC, PS)

 

SUNDAY : OFF

Mon

Week

2

SSM

 

SSM & SC

 

MK

 

MK & PS

 

Tues

SSM

 

SSM & SC

 

MK

 

MK & PS

 

Wed

SSM

 

SSM & SC

 

MK

 

MK & PS

 

Thu

SSM

 

SSM & SC

 

MK

 

MK & PS

 

Fri

SSM

 

SSM & SC

 

MK

 

MK & PS

 

Sat

Tutorial
(NKJ, SC, PS)

 

Tutorial
(NKJ, SC, PS)

 

Tutorial
(NKJ, SC, PS)

 

Tutorial
(NKJ, SC, PS)

 

SUNDAY : OFF

Mon

Week

3

AG

 

AG & SC

 

AB2

 

AB2 & PS

 

Tues

AG

 

AG & SC

 

AB2

 

AB2 & PS

 

Wed

AG

 

AG & SC

 

AB2

 

AB2 & PS

 

Thu

AG

 

AG & SC

 

AB2

 

AB2 & PS

 

Fri

AG

 

AG & SC

 

AB2

 

AB2 & PS

 

Sat

Feedback collection and concluding session

Selected Applicants: 

 Instructions for Local participants: No accommodation will be arranged.

Serial SID Full Name Gender Affiliation Position in College/ University University/Institute M.Sc./ M.A. Year of Passing M.Sc./ M.A Ph.D. Degree Date
1 48078 Mr. Utsav Dewan Male Indian Statistical Institute, Kolkata PhD Student Indian Statistical Institute, Kolkata 2020  
2 48216 Mr. Bipattaran Mandal Male Indian Institute of Technology Jodhpur MSc Student Indian Institute of Technology Jodhpur Appeared  
3 48329 Mr. Ashif Khan Male Indian Institute of Technology Gandhinagar PhD University of Hyderabad 2021  
4 48274 Mr. Hemant Bansal Male IISER Mohali PhD Student TIFR CAM 2020  
5 48357 Mr. Dhruba Prakash Biswas Male University of Calcutta PhD Scholar M.Sc. (University of Calcutta) 2019  
6 48405 Mr. Jyotirmay Das Male TCG Centres for Research and Education in Science and Technology PhD Student National Institute of Technology Rourkela 2022  
7 48583 Ms Manali Sajjan Female IIT Guwahati PhD University of Calcutta 2019  
8 48751 Mr. Aniket Basak Male IISER Berhampur BS-MS (Dual degree) 4th year student IISER Berhampur Appeared  
9 48888 Ms. Aparna Ramgopal Sharma Female South Asian University, New Delhi MSc Student South Asian University, New Delhi Appeared  
10 48966 Mr. Pradeep Vishwakarma Male Indian Institute of Technology Bhilai PhD IISER Kolkata 2022  
11 48968 Ms. Manisha Female Indian Institute of Technology Bhilai PhD student Central University of Haryana 2020  
12 49244 Mr Arvind Kumar Nath Male Indian Institute of Technology, Kanpur PhD Indian Institute of Technology, Gandhinagar 2018  
13 49279 Mr. Mangala Prasad Male IIT Kanpur PhD Student IIT Kannpur 2021  
14 49287 Mr Anubrato Bhattacharyya Male Presidency University PhD Tifr-CAM 2020  
15 49428 Mr Ojas Kumar Male Ashoka University Fourth year bachelors student Postgraduate Diplomma (DipASR): Advanced Major in Mathematics Appeared  
16 49462 Ms. Annesha Deb Female Indian Institute of Technology, Kanpur PhD University of Delhi 2022  
17 49484 Mr. Aniruddhan Ganesaraman Male Indian Statistical Institute M.Stat. student Indian Statistical Institute    
18 49591 Mr. Sarikul Islam Male IIT Kharagpur PhD Scholar Aligarh Muslim University, Aligarh 2020  
19 49601 Mr Mohit Kumar Chaubey Male Indian Institute of technology,Indore M.Sc Student indian institute of technology indore Appeared  
20 49636 Mr. Arkajit Pal Choudhury Male Indian Statistical Institute Kolkata SRF Mathematics Indian Statistical Institute, Kolkata 2020  
21 49640 Mr Uttaran Chatterjee Male Indian Statistical institute Msc Student Indian Statistical Institute    
22 49685 Ms. Nishi Thakur Female Indian Institute of Technology, Indore MSc student Indian Institute of Technology Indore Appeared  
23 49782 Mr. Agniva Dey Male Ramakrishna Mission Vivekananda Centenary College MSc Student Ramakrishna Mission Vivekananda Centenary College Appeared  
  Local  participant
1 48951 Ms. Naligeti Vaishnavi Female National Institue of Science Education and Research, Bhubaneswar Integrated M.Sc. Student      
2 49148 Dr Mohit Tripathi Male NISER Post-doctoral Fellow IIT Guwahati 2015 19/01/2021
3 49650 Ms. Sunita Rani Female IIT Bhubaneswar PhD Student Kurukshetra University,Kurukshetra 2018  
  Waiting   List  
1 48305 Mr Anan Saha Male Indian Institute of Technology, Tirupati MSc Student Indian Institute of Technology Tirupati MSc Appeared  
2 49283 Mr. Satya Sai Aditya Duggaraju Male Indian Institute of Technology, Bhilai MSc Student Indian Institute of Technology, Bhilai    
3 49553 Ms. Sapna Kushwaha Female dr. harisingh gour (central)university, sagar MSc student      
4 49649 Mr. Pradyumna Kumar Dhar Male IIT TIRUPATI m.sc IIT TIRUPATI Appeared  
5 48600 Ms. Kalpana Rawat Female Indian Institute Of Space Science And Technology PhD Student Kumaun University, Nainital, Uttarakhand 2020  

 

 

How to Reach: 

Click the following link for more information: https://www.niser.ac.in/content/how-reach
NISER Bhubaneswar is located at Jatni, which is around 30 km from Bhubaneswar City/Railway station (BBS). The nearest railway station is: Khurda Road Junction (KUR), which is around 4 km from NISER. One can avail auto-rickshaw service or state run road transportation buses from both the train stations (towards Khurda) to reach NISER. The nearest airport is: Biju Patnaik International Airport (BBI), which is around 28 km from NISER. One can avail Ola or pre-paid taxi service from the airport to reach NISER. See Map

School Short Name: 

sp

Last Date Application: 

Sunday, May 14, 2023

School Type: 

AIS

Separate faculty form: 

0