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Course Co-ordinated by IIT Delhi
Coordinators
 
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, 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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