X
X
X

X
Courses » Stochastic Processes - 1

Stochastic Processes - 1

ABOUT THE COURSE

This course explanations and expositions of stochastic processes concepts which they need for their experiments and research. It also covers theoretical concepts pertaining to handling various stochastic modeling. This course provides classification and properties of stochastic processes, discrete and continuous time Markov chains and simple Markovian queueing models and applications of CTMC.

INTENDED AUDIENCE

BE, ME, BSc, MSc, PhD

PRE-REQUISITES

A basic course on Probability.

INDUSTRY SUPPORT – LIST OF COMPANIES/INDUSTRY THAT WILL RECOGNIZE/VALUE THIS ONLINE COURSE

Goldman Sachs, FinMachenics, Deutsche Bank and other finance companies.

659 students have enrolled already!!

COURSE INSTRUCTOR



S. Dharmaraja earned his M.Sc. degree in Applied Mathematics from Anna University, Madras, India, in 1994 and Ph.D. degree in Mathematics from the Indian Institute of Technology Madras, in 1999. From 1999 to 2002, he was a post-doctoral fellow at the Department of Electrical and Computer Engineering, Duke University, USA. From 2002 to 2003, he was a research associate at the TRLabs, Winnipeg, Canada.

He has been with the Department of Mathematics, IIT Delhi, since 2003, where he is currently a Professor and Head, Department of Mathematics and joint faculty of Bharti School of Telecommunication Technology and Management. He appointed as 'Jaswinder & Tarvinder Chadha Chair Professor' for teaching and research in the area of Operations Research from May 2010 to July 2015. He has held visiting positions at the Duke University, USA, University of Calgary, Canada, University of Los Andes, Bogota, Colombia, National University of Colombia, Bogota, Colombia, University of Verona, Verona, Italy, Sungkyunkwan University, Suwon,Korea and Universita degli Studi di Salerno, Fisciano, Italy.

His research interests include applied probability, queueing theory, stochastic modeling, performance analysis of computer and communication systems and financial mathematics. He has published over 30 papers in refereed international journals and over 20 papers in refereed international conferences in these areas. He is an Associate Editor of International Journal of Communication Systems. Recently, he is co-author of a text book entitled "Introduction to Probability and Stochastic Processes with Applications" in John Wiley and co-author of a text book entitled "Financial Mathematics: An Introduction" in Narosa.

MORE DETAILS ABOUT THE COURSE
Course url: https://onlinecourses.nptel.ac.in/noc16_ma08
Course duration : 08 weeks
Start date and end date of course: 18 July 2016 - 9 September 2016
Dates of exams :  18 September 2016 & 25 September 2016
Time of exam : 2pm - 5pm
Final List of exam cities will be available in exam registration form.
Exam registration url - Will be announced shortly
Exam Fee: The online registration form has to be filled and the certification exam fee of approximately Rs 1000(non-Programming)/1250(Programming) needs to be paid.

CERTIFICATE

E-Certificate will be given to those who register and write the exam. Certificate will have your name, photograph and the score in the final exam. It will have the logos of NPTEL and IIT Delhi.
It will be e-verifiable at nptel.ac.in/noc.

COURSE LAYOUT

Week 1: Probability theory refresher
  1. Introduction to stochastic process
  2. Introduction to stochastic process (contd.)
Week 2: Probability theory refresher (contd.)
  1. Problems in random variables and distributions
  2. Problems in Sequence of random variables
Week 3: Definition and simple stochastic process
  1. Definition, classification and Examples
  2. Simple stochastic processes
Week 4: Discrete-time Markov chains
  1. Introduction, Definition and Transition Probability Matrix
  2. Chapman-Kolmogorov Equations
  3. Classification of States and Limiting Distributions
Week 5: Discrete-time Markov chains (contd.)
  1. Limiting and Stationary Distributions
  2. Limiting Distributions, Ergodicity and stationary distributions
  3. Time Reversible Markov Chain, Application of Irreducible Markov chains in Queueing Models
  4. Reducible Markov Chains
Week 6: Continuous-time Markov chains
  1. Definition, Kolmogrov Differential Equation and Infinitesimal Generator Matrix
  2. Limiting and Stationary Distributions, Birth Death Processes
  3. Poisson processes
Week 7: Simple Markovian Queueing Models
  1. M/M/1 Queueing model
  2. Simple Markovian Queueing Models
Week 8: Applications of Continuous-time Markov Chains
  1. Queueing networks
  2. Communication systems
  3. Stochastic Petri Nets
REFERENCE BOOKS

1. J Medhi, Stochastic Processes, 3rd edition, New Age International Publishers, 2009
2. Liliana Blanco Castaneda, Viswanathan Arunachalam, Selvamuthu Dharmaraja, Introduction to Probability and Stochastic Processes with Applications, Wiley, 2012.
3. Kishor S. Trivedi, Probability and Statistics with Reliability, Queuing, and Computer Science Applications, 2nd Edition, Wiley, 2002.