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February 4th, 2017, 02:17 PM
Super Moderator
 
Join Date: Mar 2012
Re: IIT Delhi MOOC

The Indian Institute of Technology Delhi is an open building establishment situated in Delhi, India. It is one of the IITs alongside other Indian Institutes of Technology establishments in India

"MOOC" remains for Massive Open Online Course. Generally these online courses are educated by colleges all around the globe

They are accessible for anybody with a web association. A portion of the well known MOOC suppliers incorporate Coursera, edX, Udacity, and FutureLearn. They band together with colleges, organizations, and teachers to give MOOCs.

MOOCs are intended for an online group of onlookers, instructing basically through short (5–20 min.) pre-recorded video addresses. You watch these recordings on a week by week plan when it is advantageous for you. MOOCs likewise have understudy talk discussions, homework/assignments, and online tests or exams.

Stochastic Processes at IIT, Delhi through MOOC's

This course clarifications and compositions of stochastic procedures ideas which they requirement for their examinations and research. It likewise covers hypothetical ideas relating to taking care of different stochastic demonstrating. This course gives arrangement and properties of stochastic procedures, discrete and ceaseless time Markov chains, basic Markovian queueing models, uses of CTMC, martingales, Brownian movement, restoration forms, spreading forms, stationary and autoregressive procedures.

Syllabus

Week 1:Probability theory refresher

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

Week 2:Probability theory refresher (contd.)

Problems in random variables and distributions
Problems in Sequence of random variables

Week 3efinition and simple stochastic process

Definition, classification and Examples
Simple stochastic processes

Week 4iscrete-time Markov chains

Introduction, Definition and Transition Probability Matrix
Chapman-Kolmogorov Equations
Classification of States and Limiting Distributions

Week 5iscrete-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

Week 6:Continuous-time Markov chains

Definition, Kolmogrov Differential Equation and Infinitesimal Generator Matrix
Limiting and Stationary Distributions, Birth Death Processes
Poisson processes

Week 7:Continuous-time Markov Chains (contd.)

M/M/1 Queueing model
Simple Markovian Queueing Models

Week 8:Applications of CTMC

Queueing networks
Communication systems
Stochastic Petri Nets

Week 9:Martingales

Conditional Expectation and filteration
Definition and simple examples

Week 10:Brownian Motion

Definition and Properties
Processes Derived from Brownian Motion
Stochastic Differential Equation

Week 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

Week 12:Branching Processes, Stationary and Autoregressive Processes


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