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Course11110201439 lectures

Stochastic Processes

Dr. S. Dharmaraja · IIT Delhi

Start with lecture 1 At NPTEL

Lectures

Probability Theory Refresher

  1. Introduction to Stochastic Processes Video
  2. Introduction to Stochastic Processes (Contd.) Video
  3. Problems in Random Variables and Distributions Video
  4. Problems in Sequences of Random Variables Video

Definition and Simple Stochastic Processes

  1. Definition, Classification and Examples Video
  2. Simple Stochastic Processes Video

Stationary and Auto Regressive Processes

  1. Stationary Processes Video
  2. Autoregressive Processes Video

Discrete-time Markov Chain

  1. Introduction, Definition and Transition Probability Matrix Video
  2. Chapman-Kolmogrov Equations Video
  3. Classification of States and Limiting Distributions Video
  4. Limiting and Stationary Distributions Video
  5. Limiting Distributions, Ergodicity and Stationary Distributions Video
  6. Time Reversible Markov Chain, Application of Irreducible Markov Chain in Queueing Models Video
  7. Reducible Markov Chains Video

Continuous-time Markov Chain

  1. Definition, Kolmogrov Differential Equations and Infinitesimal Generator Matrix Video
  2. Limiting and Stationary Distributions, Birth Death Processes Video
  3. Poisson Processes Video
  4. M/M/1 Queueing Model Video
  5. Simple Markovian Queueing Models Video
  6. Queueing Networks Video
  7. Communication Systems Video
  8. Stochastic Petri Nets Video

Martingales

  1. Conditional Expectation and Filtration Video
  2. Definition and Simple Examples Video

Brownian Motion and its Applications

  1. Definition and Properties Video
  2. Processes Derived from Brownian Motion Video
  3. Stochastic Differential Equations Video
  4. Ito Integrals Video
  5. Ito Formula and its Variants Video
  6. Some Important SDE`s and Their Solutions Video

Renewal Processes

  1. Renewal Function and Renewal Equation Video
  2. Generalized Renewal Processes and Renewal Limit Theorems Video
  3. Markov Renewal and Markov Regenerative Processes Video
  4. Non Markovian Queues Video
  5. Non Markovian Queues Cont,, Video
  6. Application of Markov Regenerative Processes Video

Branching Processes

  1. Galton-Watson Process Video
  2. Markovian Branching Process Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Delhi
Department
Mathematics
Teacher
Dr. S. Dharmaraja
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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