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Course Co-ordinated by IIT Delhi
Dr. S. Dharmaraja
IIT Delhi


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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.


Topics and Contents


Probability theory refresher

  1. Introduction to stochastic process.
  2. Introduction to stochastic process (contd.).


Probability theory refresher (contd.)

  1. Problems in random variables and distributions
  2. Problems in Sequence of random variables.


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.


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.

A basic course on Probability.

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.

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