# Applied Stochastic Processes

- Institution: IIT Kharagpur
- Department: Mathematics
- Teacher: Prof. Swanand Ravindra Khare Prof. Amitalok Jayant Budkuley
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111105901)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111105901)
- Who can watch: Teens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Lecture 01 : Introduction to Probability](https://invisiblenetwork.ai/learn/nptel/111105901/af0637377a17) (Video)
2. [Lecture 02 : Conditional Probability](https://invisiblenetwork.ai/learn/nptel/111105901/6ee7da11b80a) (Video)
3. [Lecture 03 : Total Probability and Bayes’ Rule](https://invisiblenetwork.ai/learn/nptel/111105901/5c98acb3dcf7) (Video)
4. [Lecture 04 : Random Variables (Discrete)](https://invisiblenetwork.ai/learn/nptel/111105901/37d7b21a63d5) (Video)
5. [Lecture 05 : Discrete Random Variables & Special Distributions](https://invisiblenetwork.ai/learn/nptel/111105901/6b72da2034ed) (Video)
6. [Lecture 6 : Continuous Random Variables](https://invisiblenetwork.ai/learn/nptel/111105901/d70bf7da42cb) (Video)
7. [Lecture 7 : Expectation, Variance and Joint Distributions](https://invisiblenetwork.ai/learn/nptel/111105901/c91ee4d48066) (Video)
8. [Lecture 8 : Conditional pmfs and pdfs, Independence](https://invisiblenetwork.ai/learn/nptel/111105901/d431b482c212) (Video)
9. [Lecture 9 : Conditional Expectation and Conditional Variance](https://invisiblenetwork.ai/learn/nptel/111105901/88ad055e7606) (Video)
10. [Lecture 10 : Functions of random variable, sampling, limit theorems](https://invisiblenetwork.ai/learn/nptel/111105901/6c6b3697b85e) (Video)
11. [Lecture 11 : Introduction to Stochastic Processes, Hitting Time](https://invisiblenetwork.ai/learn/nptel/111105901/a7c39eccd56a) (Video)
12. [Lecture 12 : Markov Chains](https://invisiblenetwork.ai/learn/nptel/111105901/f9b030632d52) (Video)
13. [Lecture 13 : Chapman–Kolmogorov Equations](https://invisiblenetwork.ai/learn/nptel/111105901/55e8b4bd33f5) (Video)
14. [Lecture 14 : Classification of States](https://invisiblenetwork.ai/learn/nptel/111105901/03c945393bcc) (Video)
15. [Lecture 15 : Limiting and Stationary Distributions](https://invisiblenetwork.ai/learn/nptel/111105901/daaa483bdbd6) (Video)
16. [Lecture 16 : Existence and Uniqueness of Stationary Distributions](https://invisiblenetwork.ai/learn/nptel/111105901/b979e0b48c60) (Video)
17. [Lecture 17 : Positive and Null Recurrence](https://invisiblenetwork.ai/learn/nptel/111105901/804797107be1) (Video)
18. [Lecture 18 : Computation of Stationary Distribution and Gambler's Ruin](https://invisiblenetwork.ai/learn/nptel/111105901/e1c1aec3bfbf) (Video)
19. [Lecture 19 : Mean Time in Transient States and Branching Processes](https://invisiblenetwork.ai/learn/nptel/111105901/9ada3a61a6e6) (Video)
20. [Lecture 20 : Hidden Markov Models](https://invisiblenetwork.ai/learn/nptel/111105901/a913a7521214) (Video)
21. [Lecture 21 : Introduction to counting processes and Bernoulli random processes](https://invisiblenetwork.ai/learn/nptel/111105901/a866db557c90) (Video)
22. [Lecture 22 : Foundations of discrete-time Bernoulli random processes](https://invisiblenetwork.ai/learn/nptel/111105901/0945bc3f686b) (Video)
23. [Lecture 23 : Bernoulli random processes: Alternate synthesis approaches](https://invisiblenetwork.ai/learn/nptel/111105901/bae3b5c09dbc) (Video)
24. [Lecture 24 : Counting function of Bernoulli random processes](https://invisiblenetwork.ai/learn/nptel/111105901/96c77e9a73cd) (Video)
25. [Lecture 25 : Operations on Bernoulli random processes, and summary](https://invisiblenetwork.ai/learn/nptel/111105901/5cf45fed26bc) (Video)
26. [Lecture 26 : Foundations of continuous-time Poisson random processes](https://invisiblenetwork.ai/learn/nptel/111105901/45ffd146d533) (Video)
27. [Lecture 27 : Poisson counting processes: Dynamical system approach, counting function](https://invisiblenetwork.ai/learn/nptel/111105901/849a43817ada) (Video)
28. [Lecture 28 : Bernoulli approximation of Poisson processes, Key properties and illustrations via counting functions of Poisson counting processes](https://invisiblenetwork.ai/learn/nptel/111105901/a532ea3ec832) (Video)
29. [Lecture 29 : Operations on Poisson counting processes, Illustrative examples](https://invisiblenetwork.ai/learn/nptel/111105901/3691a9e94cf0) (Video)
30. [Lecture 30 : Illustrative examples involving Poisson counting processes, summary, and comparison of Bernoulli and Poisson counting processes.](https://invisiblenetwork.ai/learn/nptel/111105901/aa09ec9bf2c3) (Video)
31. [Lecture 31 : Continuous-time Markov Chains (CTMCs): Introduction](https://invisiblenetwork.ai/learn/nptel/111105901/d1ac39b5e4a7) (Video)
32. [Lecture 32 : CTMCs Foundations 1: Formal definitions of important quantities associated with CTMCs](https://invisiblenetwork.ai/learn/nptel/111105901/f8f4c34dd513) (Video)
33. [Lecture 33 : CTMCs Foundations 2: Transition rates, Generator, Embedded chains](https://invisiblenetwork.ai/learn/nptel/111105901/9f992217afab) (Video)
34. [Lecture 34 : CTMCs via a sequence of DTMCs](https://invisiblenetwork.ai/learn/nptel/111105901/8a4749c5a405) (Video)
35. [Lecture 35 : Birth-Death CTMCs: Foundations](https://invisiblenetwork.ai/learn/nptel/111105901/fd6eef9592be) (Video)
36. [Lecture 36 : Birth-Death CTMCs: Illustrations](https://invisiblenetwork.ai/learn/nptel/111105901/b452aa350ce5) (Video)
37. [Lecture 37 : CTMCs: A re-look using first principles approach (I)](https://invisiblenetwork.ai/learn/nptel/111105901/6f76e1bf4f26) (Video)
38. [Lecture 38 : CTMCs: A re-look using first principles approach (II)](https://invisiblenetwork.ai/learn/nptel/111105901/b8ca9c3d25d3) (Video)
39. [Lecture 39 : Transient analysis of CTMCs](https://invisiblenetwork.ai/learn/nptel/111105901/3c1fecec3132) (Video)
40. [Lecture 40 : Steady state analysis of CTMCs, Reversibility, birth-death chains and reversibility](https://invisiblenetwork.ai/learn/nptel/111105901/42de343143fa) (Video)
41. [Lecture 41 : Renewal process: Foundations, examples, applications](https://invisiblenetwork.ai/learn/nptel/111105901/7e8a4f597abb) (Video)
42. [Lecture 42 : Counting function of Renewal processes](https://invisiblenetwork.ai/learn/nptel/111105901/8933e991c210) (Video)
43. [Lecture 43 : Renewal function and Elementary renewal theorem](https://invisiblenetwork.ai/learn/nptel/111105901/9de58a8b2383) (Video)
44. [Lecture 44 : CLT for Renewal processes, Renewal reward theorem, Illustration via age of renewal](https://invisiblenetwork.ai/learn/nptel/111105901/a333ca1133df) (Video)
45. [Lecture 45 : Renewal process: Illustrations and extensions](https://invisiblenetwork.ai/learn/nptel/111105901/7be504e37f1a) (Video)
46. [Lecture 46 : Queuing theory: Foundations, applications, Illustrative example via timing diagram](https://invisiblenetwork.ai/learn/nptel/111105901/de3e633366f8) (Video)
47. [Lecture 47 : Discrete-time Queues: Geo/Geo/1 queues](https://invisiblenetwork.ai/learn/nptel/111105901/e2b820505b1f) (Video)
48. [Lecture 48 : Continuous-time Queues: M/M/* queues](https://invisiblenetwork.ai/learn/nptel/111105901/d82df485bb40) (Video)
49. [Lecture 49 : Delay models and delay analysis in Queueing theory](https://invisiblenetwork.ai/learn/nptel/111105901/0aadecc9a1c4) (Video)
50. [Lecture 50 : Queueing Theory: General queues, Burke's theorem, Tandem queues, examples](https://invisiblenetwork.ai/learn/nptel/111105901/184e6e120f74) (Video)
51. [Lecture 51 : Introduction to Brownian Motion and Random Walks](https://invisiblenetwork.ai/learn/nptel/111105901/50453dab34ee) (Video)
52. [Lecture 52 : Properties and Joint Distributions of Brownian Motion](https://invisiblenetwork.ai/learn/nptel/111105901/08fc2e50ee4a) (Video)
53. [Lecture 53 : White Noise and Stochastic Integrals](https://invisiblenetwork.ai/learn/nptel/111105901/ed1bcbefc140) (Video)
54. [Lecture 54 : Gaussian Processes and Brownian Bridge](https://invisiblenetwork.ai/learn/nptel/111105901/7fc5d159e1d4) (Video)
55. [Lecture 55 : Stationary Processes and Random Telegraph Signal](https://invisiblenetwork.ai/learn/nptel/111105901/1b9a928831d4) (Video)
56. [Lecture 56 : Second-Order Stationarity and Auto-Regressive Processes](https://invisiblenetwork.ai/learn/nptel/111105901/63b63aab7467) (Video)
57. [Lecture 57 : Linear Systems and Spectral Density](https://invisiblenetwork.ai/learn/nptel/111105901/de21677eeaaa) (Video)
58. [Lecture 58 : Pricing Stock Options & Arbitrage Theorem](https://invisiblenetwork.ai/learn/nptel/111105901/91f60efeedf7) (Video)
59. [Lecture 59 : Martingales and Geometric Brownian Motion](https://invisiblenetwork.ai/learn/nptel/111105901/82a620a74da1) (Video)
60. [Lecture 60 : Black-Scholes Formula & Jump Processes](https://invisiblenetwork.ai/learn/nptel/111105901/98066936e8e3) (Video)