Course Co-ordinated by IIT Delhi
 Coordinators 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, simple Markovian queueing models, applications of CTMC, martingales, Brownian motion, renewal processes, branching processes, stationary and autoregressive processes.

 Week Topics 1. Probability theory refresher Introduction to stochastic process Introduction to stochastic process (contd.) 2. Probability theory refresher (contd.) Problems in random variables and distributions Problems in Sequence of random variables 3. Definition and simple stochastic process Definition, classification and Examples Simple stochastic processes 4. Discrete-time Markov chains Introduction, Definition and Transition Probability Matrix Chapman-Kolmogorov Equations Classification of States and Limiting Distributions 5. 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 6. Continuous-time Markov chains Definition, Kolmogrov Differential Equation and Infinitesimal Generator Matrix Limiting and Stationary Distributions, Birth Death Processes Poisson processes 7. Continuous-time Markov Chains (contd.) M/M/1 Queueing model Simple Markovian Queueing Models 8. Applications of CTMC Queueing networks Communication systems Stochastic Petri Nets 9. Martingales Conditional Expectation and filteration Definition and simple examples 10. Brownian Motion Definition and Properties Processes Derived from Brownian Motion 11. 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 12. Branching Processes, Stationary and Autoregressive Processes

A basic course on Probability

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