# Introduction to Stochastic Processes - Institution: IIT Bombay - Department: Management - Teacher: Prof. Manjesh Hanawal - Level: Undergraduate - Language: English - Subjects: Business and management - Source: [NPTEL](https://nptel.ac.in/courses/110101141) - Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.) - Syllabus: [at the source](https://nptel.ac.in/courses/110101141) - Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words) ## Lectures 1. [Lecture 1: Sample Space and events](https://invisiblenetwork.ai/learn/nptel/110101141/7b74883fa5a3) (Video) 2. [Lecture 2: Axioms of Probability](https://invisiblenetwork.ai/learn/nptel/110101141/9dfd5eba2cc0) (Video) 3. [Lecture 3: Independence of events and Conditional Probability](https://invisiblenetwork.ai/learn/nptel/110101141/3ded27873c28) (Video) 4. [Lecture 4: Baye's Theorem and Introduction to Random Variables](https://invisiblenetwork.ai/learn/nptel/110101141/0d83f2056466) (Video) 5. [Lecture 5: CDF and it's properties](https://invisiblenetwork.ai/learn/nptel/110101141/05cc5be8e1ae) (Video) 6. [Lecture 6: Continuity of Probability](https://invisiblenetwork.ai/learn/nptel/110101141/bd5f033e25ee) (Video) 7. [Lecture 7: Discrete and Continuous random variables](https://invisiblenetwork.ai/learn/nptel/110101141/e741493e31eb) (Video) 8. [Lecture 8: Expectation of random variables and its properties](https://invisiblenetwork.ai/learn/nptel/110101141/50d7d874ecb1) (Video) 9. [Lecture 9: Variance and some inequalities of random variables](https://invisiblenetwork.ai/learn/nptel/110101141/20178da7167f) (Video) 10. [Lecture 10: Discrete Probability Distributions](https://invisiblenetwork.ai/learn/nptel/110101141/e3bdd320cff3) (Video) 11. [Lecture 11: Continuous Probability Distributions](https://invisiblenetwork.ai/learn/nptel/110101141/086d93d7041c) (Video) 12. [Lecture 12: Jointly distributed random variables and conditional distributions](https://invisiblenetwork.ai/learn/nptel/110101141/0277ce6173c8) (Video) 13. [Lecture 13: Correlation and Covariance](https://invisiblenetwork.ai/learn/nptel/110101141/6b817b4f5155) (Video) 14. [Lecture 14: Transformation of random vectors](https://invisiblenetwork.ai/learn/nptel/110101141/c13a1f6c62bc) (Video) 15. [Lecture 15: Gaussian random vector and joint Gaussian distribution](https://invisiblenetwork.ai/learn/nptel/110101141/0b149432967b) (Video) 16. [Lecture 16: Random Processes](https://invisiblenetwork.ai/learn/nptel/110101141/1bc2bd65dba9) (Video) 17. [Lecture 17: Properties of random Process](https://invisiblenetwork.ai/learn/nptel/110101141/78ad8a8eb5d6) (Video) 18. [Lecture 18: Poisson Process](https://invisiblenetwork.ai/learn/nptel/110101141/07199510d01a) (Video) 19. [Lecture 19: Properties of Poisson Process (Part 1)](https://invisiblenetwork.ai/learn/nptel/110101141/9c96d5c8d372) (Video) 20. [Lecture 20: Properties of Poisson Process (Part 2)](https://invisiblenetwork.ai/learn/nptel/110101141/13eac1c3ca6c) (Video) 21. [Lecture 21: Convergence of sequence of random variables (Part 1)](https://invisiblenetwork.ai/learn/nptel/110101141/d28edb4edadb) (Video) 22. [Lecture 22: Convergence of sequence of random variables (Part 2)](https://invisiblenetwork.ai/learn/nptel/110101141/bdcd66dee1c1) (Video) 23. [Lecture 23: Relation between different notions of convergence](https://invisiblenetwork.ai/learn/nptel/110101141/f19e6e082266) (Video) 24. [Lecture 24: Cauchy's criteria of convergence](https://invisiblenetwork.ai/learn/nptel/110101141/0d5e20747af9) (Video) 25. [Lecture 25: Convergence in expectation](https://invisiblenetwork.ai/learn/nptel/110101141/bc06d86fdfab) (Video) 26. [Lecture 26: Law of Large Numbers](https://invisiblenetwork.ai/learn/nptel/110101141/6d7853cd018b) (Video) 27. [Lecture 27: Central limit theorem](https://invisiblenetwork.ai/learn/nptel/110101141/59719467f867) (Video) 28. [Lecture 28: chernoff bound](https://invisiblenetwork.ai/learn/nptel/110101141/a830741577d3) (Video) 29. [Lecture 29: Introduction to Markov property](https://invisiblenetwork.ai/learn/nptel/110101141/cde4efa30776) (Video) 30. [Lecture 30: Transition Probability Matrix](https://invisiblenetwork.ai/learn/nptel/110101141/3c9e0cc25470) (Video) 31. [Lecture 31: Finite dimensional distribution of Markov chains](https://invisiblenetwork.ai/learn/nptel/110101141/223dc8084892) (Video) 32. [Lecture 32: Strong Markov Property](https://invisiblenetwork.ai/learn/nptel/110101141/9d048205d394) (Video) 33. [Lecture 33: Stopping Time](https://invisiblenetwork.ai/learn/nptel/110101141/2bcfe57a5bfb) (Video) 34. [Lecture 34: Hitting Times and Recurrence](https://invisiblenetwork.ai/learn/nptel/110101141/106671596a71) (Video) 35. [Lecture 35: Mean Number of returns to a state](https://invisiblenetwork.ai/learn/nptel/110101141/91187e6da122) (Video) 36. [Lecture 36: Communicating classes and class properties](https://invisiblenetwork.ai/learn/nptel/110101141/2cc9f7722b2d) (Video) 37. [Lecture 37: Class Properties Continued](https://invisiblenetwork.ai/learn/nptel/110101141/6351cadd0ccd) (Video) 38. [Lecture 38: Positive Recurrence and The Invariant Probability Vector](https://invisiblenetwork.ai/learn/nptel/110101141/4dcac46dc659) (Video) 39. [Lecture 39: Properties of Invariant Probability Vector](https://invisiblenetwork.ai/learn/nptel/110101141/f31e0487efe8) (Video) 40. [Lecture 40: Condition For Transience](https://invisiblenetwork.ai/learn/nptel/110101141/b4d21ac7da89) (Video) 41. [Lecture 41: Example of Queue](https://invisiblenetwork.ai/learn/nptel/110101141/6f67b63f4695) (Video) 42. [Lecture 42: Queue Continued and Example of Page Rank](https://invisiblenetwork.ai/learn/nptel/110101141/96a27fa11763) (Video) 43. [Lecture 43: Introduction to renewal Theory](https://invisiblenetwork.ai/learn/nptel/110101141/949e30a3f64f) (Video) 44. [Lecture 44: The Elementary Renewal Theorem](https://invisiblenetwork.ai/learn/nptel/110101141/97949666e5d2) (Video) 45. [Lecture 45: Application to DTMC](https://invisiblenetwork.ai/learn/nptel/110101141/e98d695d9be4) (Video) 46. [Lecture 46: Renewal Reward Theorem](https://invisiblenetwork.ai/learn/nptel/110101141/c8dcafb92f8a) (Video) 47. [Lecture 47: Introduction to Continuous Time Markov Chains](https://invisiblenetwork.ai/learn/nptel/110101141/a786d5382cc9) (Video) 48. [Lecture 48: Properties of states in CTMC](https://invisiblenetwork.ai/learn/nptel/110101141/d34f48677451) (Video) 49. [Lecture 49: Embedded markov chain](https://invisiblenetwork.ai/learn/nptel/110101141/313c59abd644) (Video) 50. [Live Session 18-02-2020](https://invisiblenetwork.ai/learn/nptel/110101141/7b74883fa5a3-2) (Video)