IIT Delhi Course , Prof. S. Dharmaraja

**332**students enrolled

IIT Delhi Course , Prof. S. Dharmaraja

Probability Theory Refresher: Axiomatic construction of probability spaces, random variables and vectors, probability distributions, functions of random variables; mathematical expectations, transforms and generating functions, modes of convergence of sequences of random variables, laws of large numbers, central limit theorem;Introduction to Stochastic Processes (SPs): Definition and examples of SPs, classification of random processes according to state space and parameter space, types of SPs, elementary problems;Stationary Processes: Weakly stationary and strongly stationary processes, moving average and auto regressive processes;Discrete-time Markov Chains (DTMCs): Definition and examples of MCs, transition probability matrix, Chapman-Kolmogorov equations; calculation of n-step transition probabilities, limiting probabilities, classification of states, ergodicity, stationary distribution, transient MC; random walk and gamblers ruin problem, applications;Continuous-time Markov Chains (CTMCs): Kolmogorov- Feller differential equations, infinitesimal generator, Poisson process, birth-death process, stochastic Petri net, applications to queueing theory and communication networks;Martingales: Conditional expectations, definition and examples of martingales.

Brownian Motion: Wiener process as a limit of random walk; process derived from Brownian motion, stochastic differential equation, stochastic integral equation, Ito formula, Some important SDEs and their solutions, applications to finance;Renewal Processes: Renewal function and its properties, renewal theorems, cost/rewards associated with renewals, Markov renewal and regenerative processes, non Markovian queues, applications of Markov regenerative processes;Branching Processes: Definition and examples branching processes, probability generating function, mean and variance, Galton-Watson branching process, probability of extinction

Brownian Motion: Wiener process as a limit of random walk; process derived from Brownian motion, stochastic differential equation, stochastic integral equation, Ito formula, Some important SDEs and their solutions, applications to finance;Renewal Processes: Renewal function and its properties, renewal theorems, cost/rewards associated with renewals, Markov renewal and regenerative processes, non Markovian queues, applications of Markov regenerative processes;Branching Processes: Definition and examples branching processes, probability generating function, mean and variance, Galton-Watson branching process, probability of extinction

Up Next

You can skip ad in

SKIP AD >

Advertisement

- 2x
- 1.5x
- 1x
- 0.5x
- 0.25x

EMBED LINK

COPY

DIRECT LINK

COPY

PRIVATE CONTENT

OK

Enter password to view

Please enter valid password!

- Play Pause
- Mute UnMute
- Fullscreen Normal
- @Your Company Title

0:00

3.8 (4 Ratings)

Stochastic Processes by Dr. S. Dharmaraja, Department of Mathematics, IIT Delhi. For more details on NPTEL visit httpnptel.iitm.ac.in

Heads up!

Above free video lectures are presented by IIT Delhi, under NPTEL program, there are still 6000+ iit video lectures are available.
50%

25%

25%

- 1.Introduction to Stochastic Processes
- 2.Introduction to Stochastic Processes (Contd.)
- 3.Problems in Random Variables and Distributions
- 4.Problems in Sequences of Random Variables
- 5.Definition, Classification and Examples
- 6.Simple Stochastic Processes
- 7.Stationary Processes
- 8.Autoregressive Processes
- 9.Introduction, Definition and Transition Probability Matrix
- 10.Chapman-Kolmogrov Equations
- 11.Classification of States and Limiting Distributions
- 12.Limiting and Stationary Distributions
- 13.Limiting Distributions, Ergodicity and Stationary Distributions
- 14.Time Reversible Markov Chain
- 15.Reducible Markov Chains
- 16.Definition, Kolmogrov Differential Equations and Infinitesimal Generator Matrix
- 17.Limiting and Stationary Distributions, Birth Death Processes
- 18.Poisson Processes
- 19.MM1 Queueing Model
- 20.Simple Markovian Queueing Models
- 21.Queueing Networks
- 22.Communication Systems
- 23.Stochastic Petri Nets
- 24.Conditional Expectation and Filtration
- 25.Definition and Simple Examples
- 26.Definition and Properties
- 27.Processes Derived from Brownian Motion
- 28.Stochastic Differential Equations
- 29.Ito Integrals
- 30.Ito Formula and its Variants
- 31.Some Important SDE`s and Their Solutions
- 32.Renewal Function and Renewal Equation
- 33.Generalized Renewal Processes and Renewal Limit Theorems
- 34.Markov Renewal and Markov Regenerative Processes
- 35.Non Markovian Queues
- 36.Non Markovian Queues Cont,,
- 37.Application of Markov Regenerative Processes
- 38.Galton-Watson Process
- 39.Markovian Branching Process

- FreeVideoLectures aim to help millions of students across the world acquire knowledge, gain good grades, get jobs, assist in getting promotions through quality learning material.

- You can write to us
- help@freevideolectures.com

2018 FreeVideoLectures. All rights reserved. FreeVideoLectures only promotes free course material from different sources, we are not endrosed by any university.