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Quick Facts

Medium Of InstructionsMode Of LearningMode Of Delivery
EnglishSelf Study, Virtual ClassroomVideo and Text Based

Courses and Certificate Fees

Certificate AvailabilityCertificate Providing Authority
yesIIT Delhi

The Syllabus

  • Probability theory refresher 
  • Introduction to stochastic process 
  • Introduction to stochastic process (contd.)

  • Probability theory refresher (contd.) 
  • Problems in random variables and distributions 
  • Problems in Sequence of random variables

  • Definition and simple stochastic process 
  • Definition, classification and Examples 
  • Simple stochastic processes

  • iscrete-time Markov chains 
  • Introduction, Definition and Transition Probability Matrix 
  • Chapman-Kolmogorov Equations 
  • Classification of States and Limiting Distributions

  • Discrete-time Markov chains (contd.) 
  • Limiting and Stationary Distributions 
  • Limiting Distributions, Ergodicity and stationary distributions 
  • Time Reversible Markov Chain, Application of Irreducible Markov chains in Queueing Models 
  • Reducible Markov Chains

  • Continuous-time Markov chains 
  • Definition, Kolmogrov Differential Equation and Infinitesimal Generator Matrix 
  • Limiting and Stationary Distributions, Birth Death Processes 
  • Poisson processes

  • Continuous-time Markov Chains (contd.) 
  • M/M/1 Queueing model

  • Applications of CTMC 
  • Queueing networks 
  • Communication systems 
  • Stochastic Petri Nets

  • Martingales 
  • Conditional Expectation and filtration 
  • Definition and simple examples

  • Brownian Motion 
  • Definition and Properties 
  • Processes Derived from Brownian Motion 
  • Stochastic Differential Equation

  • Renewal Processes Renewal Function and Equation 
  • Generalized Renewal Processes and Renewal Limit Theorems 
  • Markov Renewal and Markov Regenerative Processes 
  • Non Markovian Queues 
  • Application of Markov Regenerative Processes

  • Branching Processes
  • Stationary and Autoregressive Processes

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