Learn · Applied Stochastic Processes

Lecture 52 of 60Week 11

Lecture 52 : Properties and Joint Distributions of Brownian Motion

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

Credits and licence

From
Applied Stochastic Processes, IIT Kharagpur (at NPTEL)
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
Who can watch
Teens profiles and older. How courses are placed

All the lectures

  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
  6. Lecture 6 : Continuous Random Variables Video
  7. Lecture 7 : Expectation, Variance and Joint Distributions Video
  8. Lecture 8 : Conditional pmfs and pdfs, Independence Video
  9. Lecture 9 : Conditional Expectation and Conditional Variance Video
  10. Lecture 10 : Functions of random variable, sampling, limit theorems Video
  11. Lecture 11 : Introduction to Stochastic Processes, Hitting Time Video
  12. Lecture 12 : Markov Chains Video
  13. Lecture 13 : Chapman–Kolmogorov Equations Video
  14. Lecture 14 : Classification of States Video
  15. Lecture 15 : Limiting and Stationary Distributions Video
  16. Lecture 16 : Existence and Uniqueness of Stationary Distributions Video
  17. Lecture 17 : Positive and Null Recurrence Video
  18. Lecture 18 : Computation of Stationary Distribution and Gambler's Ruin Video
  19. Lecture 19 : Mean Time in Transient States and Branching Processes Video
  20. Lecture 20 : Hidden Markov Models Video
  21. Lecture 21 : Introduction to counting processes and Bernoulli random processes Video
  22. Lecture 22 : Foundations of discrete-time Bernoulli random processes Video
  23. Lecture 23 : Bernoulli random processes: Alternate synthesis approaches Video
  24. Lecture 24 : Counting function of Bernoulli random processes Video
  25. Lecture 25 : Operations on Bernoulli random processes, and summary Video
  26. Lecture 26 : Foundations of continuous-time Poisson random processes Video
  27. Lecture 27 : Poisson counting processes: Dynamical system approach, counting function Video
  28. Lecture 28 : Bernoulli approximation of Poisson processes, Key properties and illustrations via counting functions of Poisson counting processes Video
  29. Lecture 29 : Operations on Poisson counting processes, Illustrative examples Video
  30. Lecture 30 : Illustrative examples involving Poisson counting processes, summary, and comparison of Bernoulli and Poisson counting processes. Video
  31. Lecture 31 : Continuous-time Markov Chains (CTMCs): Introduction Video
  32. Lecture 32 : CTMCs Foundations 1: Formal definitions of important quantities associated with CTMCs Video
  33. Lecture 33 : CTMCs Foundations 2: Transition rates, Generator, Embedded chains Video
  34. Lecture 34 : CTMCs via a sequence of DTMCs Video
  35. Lecture 35 : Birth-Death CTMCs: Foundations Video
  36. Lecture 36 : Birth-Death CTMCs: Illustrations Video
  37. Lecture 37 : CTMCs: A re-look using first principles approach (I) Video
  38. Lecture 38 : CTMCs: A re-look using first principles approach (II) Video
  39. Lecture 39 : Transient analysis of CTMCs Video
  40. Lecture 40 : Steady state analysis of CTMCs, Reversibility, birth-death chains and reversibility Video
  41. Lecture 41 : Renewal process: Foundations, examples, applications Video
  42. Lecture 42 : Counting function of Renewal processes Video
  43. Lecture 43 : Renewal function and Elementary renewal theorem Video
  44. Lecture 44 : CLT for Renewal processes, Renewal reward theorem, Illustration via age of renewal Video
  45. Lecture 45 : Renewal process: Illustrations and extensions Video
  46. Lecture 46 : Queuing theory: Foundations, applications, Illustrative example via timing diagram Video
  47. Lecture 47 : Discrete-time Queues: Geo/Geo/1 queues Video
  48. Lecture 48 : Continuous-time Queues: M/M/* queues Video
  49. Lecture 49 : Delay models and delay analysis in Queueing theory Video
  50. Lecture 50 : Queueing Theory: General queues, Burke's theorem, Tandem queues, examples Video
  51. Lecture 51 : Introduction to Brownian Motion and Random Walks Video
  52. Lecture 52 : Properties and Joint Distributions of Brownian Motion Video
  53. Lecture 53 : White Noise and Stochastic Integrals Video
  54. Lecture 54 : Gaussian Processes and Brownian Bridge Video
  55. Lecture 55 : Stationary Processes and Random Telegraph Signal Video
  56. Lecture 56 : Second-Order Stationarity and Auto-Regressive Processes Video
  57. Lecture 57 : Linear Systems and Spectral Density Video
  58. Lecture 58 : Pricing Stock Options & Arbitrage Theorem Video
  59. Lecture 59 : Martingales and Geometric Brownian Motion Video
  60. Lecture 60 : Black-Scholes Formula & Jump Processes Video