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Course11110590160 lectures

Applied Stochastic Processes

Prof. Swanand Ravindra Khare Prof. Amitalok Jayant Budkuley · IIT Kharagpur

Start with lecture 1 At NPTEL

Lectures

Week 1

  1. Lecture 01 : Introduction to Probability Video
  2. Lecture 02 : Conditional Probability Video
  3. Lecture 03 : Total Probability and Bayes’ Rule Video
  4. Lecture 04 : Random Variables (Discrete) Video
  5. Lecture 05 : Discrete Random Variables & Special Distributions Video

Week 2

  1. Lecture 6 : Continuous Random Variables Video
  2. Lecture 7 : Expectation, Variance and Joint Distributions Video
  3. Lecture 8 : Conditional pmfs and pdfs, Independence Video
  4. Lecture 9 : Conditional Expectation and Conditional Variance Video
  5. Lecture 10 : Functions of random variable, sampling, limit theorems Video

Week 3

  1. Lecture 11 : Introduction to Stochastic Processes, Hitting Time Video
  2. Lecture 12 : Markov Chains Video
  3. Lecture 13 : Chapman–Kolmogorov Equations Video
  4. Lecture 14 : Classification of States Video
  5. Lecture 15 : Limiting and Stationary Distributions Video

Week 4

  1. Lecture 16 : Existence and Uniqueness of Stationary Distributions Video
  2. Lecture 17 : Positive and Null Recurrence Video
  3. Lecture 18 : Computation of Stationary Distribution and Gambler's Ruin Video
  4. Lecture 19 : Mean Time in Transient States and Branching Processes Video
  5. Lecture 20 : Hidden Markov Models Video

Week 5

  1. Lecture 21 : Introduction to counting processes and Bernoulli random processes Video
  2. Lecture 22 : Foundations of discrete-time Bernoulli random processes Video
  3. Lecture 23 : Bernoulli random processes: Alternate synthesis approaches Video
  4. Lecture 24 : Counting function of Bernoulli random processes Video
  5. Lecture 25 : Operations on Bernoulli random processes, and summary Video

Week 6

  1. Lecture 26 : Foundations of continuous-time Poisson random processes Video
  2. Lecture 27 : Poisson counting processes: Dynamical system approach, counting function Video
  3. Lecture 28 : Bernoulli approximation of Poisson processes, Key properties and illustrations via counting functions of Poisson counting processes Video
  4. Lecture 29 : Operations on Poisson counting processes, Illustrative examples Video
  5. Lecture 30 : Illustrative examples involving Poisson counting processes, summary, and comparison of Bernoulli and Poisson counting processes. Video

Week 7

  1. Lecture 31 : Continuous-time Markov Chains (CTMCs): Introduction Video
  2. Lecture 32 : CTMCs Foundations 1: Formal definitions of important quantities associated with CTMCs Video
  3. Lecture 33 : CTMCs Foundations 2: Transition rates, Generator, Embedded chains Video
  4. Lecture 34 : CTMCs via a sequence of DTMCs Video
  5. Lecture 35 : Birth-Death CTMCs: Foundations Video

Week 8

  1. Lecture 36 : Birth-Death CTMCs: Illustrations Video
  2. Lecture 37 : CTMCs: A re-look using first principles approach (I) Video
  3. Lecture 38 : CTMCs: A re-look using first principles approach (II) Video
  4. Lecture 39 : Transient analysis of CTMCs Video
  5. Lecture 40 : Steady state analysis of CTMCs, Reversibility, birth-death chains and reversibility Video

Week 9

  1. Lecture 41 : Renewal process: Foundations, examples, applications Video
  2. Lecture 42 : Counting function of Renewal processes Video
  3. Lecture 43 : Renewal function and Elementary renewal theorem Video
  4. Lecture 44 : CLT for Renewal processes, Renewal reward theorem, Illustration via age of renewal Video
  5. Lecture 45 : Renewal process: Illustrations and extensions Video

Week 10

  1. Lecture 46 : Queuing theory: Foundations, applications, Illustrative example via timing diagram Video
  2. Lecture 47 : Discrete-time Queues: Geo/Geo/1 queues Video
  3. Lecture 48 : Continuous-time Queues: M/M/* queues Video
  4. Lecture 49 : Delay models and delay analysis in Queueing theory Video
  5. Lecture 50 : Queueing Theory: General queues, Burke's theorem, Tandem queues, examples Video

Week 11

  1. Lecture 51 : Introduction to Brownian Motion and Random Walks Video
  2. Lecture 52 : Properties and Joint Distributions of Brownian Motion Video
  3. Lecture 53 : White Noise and Stochastic Integrals Video
  4. Lecture 54 : Gaussian Processes and Brownian Bridge Video
  5. Lecture 55 : Stationary Processes and Random Telegraph Signal Video

Week 12

  1. Lecture 56 : Second-Order Stationarity and Auto-Regressive Processes Video
  2. Lecture 57 : Linear Systems and Spectral Density Video
  3. Lecture 58 : Pricing Stock Options & Arbitrage Theorem Video
  4. Lecture 59 : Martingales and Geometric Brownian Motion Video
  5. Lecture 60 : Black-Scholes Formula & Jump Processes Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kharagpur
Department
Mathematics
Teacher
Prof. Swanand Ravindra Khare Prof. Amitalok Jayant Budkuley
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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