# Probabilistic Methods in PDE

- Institution: IISER Pune
- Department: Mathematics
- Teacher: Prof. Anindya Goswami
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106134)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106134)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Prerequisite Measure Theory - Part 01](https://invisiblenetwork.ai/learn/nptel/111106134/5eaba436d880) (Video)
2. [Prerequisite Measure Theory - Part 02](https://invisiblenetwork.ai/learn/nptel/111106134/a814db5f0eaf) (Video)
3. [Prerequisite Measure Theory - Part 03](https://invisiblenetwork.ai/learn/nptel/111106134/b8e8355a4adc) (Video)
4. [Random variable](https://invisiblenetwork.ai/learn/nptel/111106134/0477663a11f4) (Video)
5. [Stochastic Process](https://invisiblenetwork.ai/learn/nptel/111106134/a72055d9489e) (Video)
6. [Conditional Expectation](https://invisiblenetwork.ai/learn/nptel/111106134/4f33ea89737e) (Video)
7. [Preliminary for Stochastic Integration - Part 01](https://invisiblenetwork.ai/learn/nptel/111106134/16f6d99c2555) (Video)
8. [Preliminary for Stochastic Integration - Part 02](https://invisiblenetwork.ai/learn/nptel/111106134/02f4dc167466) (Video)
9. [Definition and properties of Stochastic Integration - Part 01](https://invisiblenetwork.ai/learn/nptel/111106134/f98fc4b27dab) (Video)
10. [Definition and properties of Stochastic Integration - Part 02](https://invisiblenetwork.ai/learn/nptel/111106134/d9e29e7df234) (Video)
11. [Further properties of Stochastic Integration](https://invisiblenetwork.ai/learn/nptel/111106134/b90158f27866) (Video)
12. [Extension of stochastic integral](https://invisiblenetwork.ai/learn/nptel/111106134/4c02d497a912) (Video)
13. [change of variable formula and proof - Part 1](https://invisiblenetwork.ai/learn/nptel/111106134/7a2525bb35b4) (Video)
14. [change of variable formula and proof - Part 2](https://invisiblenetwork.ai/learn/nptel/111106134/cd906bd63847) (Video)
15. [Brownian motion as the building block](https://invisiblenetwork.ai/learn/nptel/111106134/d3605505209d) (Video)
16. [Brownian motion and its martingale property - Part 1](https://invisiblenetwork.ai/learn/nptel/111106134/36ab76ad2bab) (Video)
17. [Brownian motion and its martingale property - Part 2](https://invisiblenetwork.ai/learn/nptel/111106134/73ff76fda44f) (Video)
18. [Application of Ito’s rule on Ito process](https://invisiblenetwork.ai/learn/nptel/111106134/86b221af1051) (Video)
19. [Harmonic function and its properties](https://invisiblenetwork.ai/learn/nptel/111106134/f8ada0e2c61f) (Video)
20. [Maximum principle of harmonic function](https://invisiblenetwork.ai/learn/nptel/111106134/bc90578ab080) (Video)
21. [Dirichlet Problem and bounded solution](https://invisiblenetwork.ai/learn/nptel/111106134/6a5fd5e38259) (Video)
22. [Example of a Dirichlet problem](https://invisiblenetwork.ai/learn/nptel/111106134/ed4018e964bb) (Video)
23. [Regular points at the boundary](https://invisiblenetwork.ai/learn/nptel/111106134/7568056c5e44) (Video)
24. [Zarembas cone condition for regularity](https://invisiblenetwork.ai/learn/nptel/111106134/4ad515bb4c79) (Video)
25. [Summary of the Zaremba's cone condition](https://invisiblenetwork.ai/learn/nptel/111106134/3212df9db0fb) (Video)
26. [Continuity of candidate solution at regular points - Part 1](https://invisiblenetwork.ai/learn/nptel/111106134/a5529790e6e8) (Video)
27. [Continuity of candidate solution at regular points - Part 2](https://invisiblenetwork.ai/learn/nptel/111106134/78ce2d60d083) (Video)
28. [Summary of bounded solution to the Dirichlet Problem](https://invisiblenetwork.ai/learn/nptel/111106134/6d246e5e18dc) (Video)
29. [Stochastic representation of bounded solution to a heat equation - Part 1](https://invisiblenetwork.ai/learn/nptel/111106134/b8e628fa721b) (Video)
30. [Stochastic representation of bounded solution to a heat equation - Part 2](https://invisiblenetwork.ai/learn/nptel/111106134/b8c1929eabd8) (Video)
31. [Uniqueness of solution to the heat equationÂ](https://invisiblenetwork.ai/learn/nptel/111106134/823fed3ec3a5) (Video)
32. [Remark on Tychonoff's Theorem](https://invisiblenetwork.ai/learn/nptel/111106134/c650e4f6c3d5) (Video)
33. [Widder’s result and its extension on heat equation](https://invisiblenetwork.ai/learn/nptel/111106134/a5e487151b4a) (Video)
34. [Solution to the mixed initial boundary value problemÂ](https://invisiblenetwork.ai/learn/nptel/111106134/d1f42aeb48e1) (Video)
35. [The Feynman-Kac formulaÂ](https://invisiblenetwork.ai/learn/nptel/111106134/facb990a9962) (Video)
36. [Kac’s theorem on the stochastic representation of solution to a second-order linear ODE - Part 1](https://invisiblenetwork.ai/learn/nptel/111106134/273ff59cf5b8) (Video)
37. [Kac’s theorem on the stochastic representation of solution to a second-order linear ODE - Part 2](https://invisiblenetwork.ai/learn/nptel/111106134/7359f6098bd2) (Video)
38. [Geometric Brownian motion](https://invisiblenetwork.ai/learn/nptel/111106134/5e65229f331a) (Video)
39. [A system of stochastic differential equations in application](https://invisiblenetwork.ai/learn/nptel/111106134/10af31af01a0) (Video)
40. [Brownian bridge](https://invisiblenetwork.ai/learn/nptel/111106134/eec48d53faf6) (Video)
41. [Simulation of stochastic differential equations](https://invisiblenetwork.ai/learn/nptel/111106134/b2c02a11214f) (Video)
42. [Stochastic differential equations: Uniqueness](https://invisiblenetwork.ai/learn/nptel/111106134/b74e4331c40d) (Video)
43. [Stochastic differential equations: Existence part 1](https://invisiblenetwork.ai/learn/nptel/111106134/662c986867a0) (Video)
44. [Stochastic differential equations: Existence part 2](https://invisiblenetwork.ai/learn/nptel/111106134/391b565589f6) (Video)
45. [Stochastic differential equations: Existence part 3](https://invisiblenetwork.ai/learn/nptel/111106134/83e88c31c13c) (Video)
46. [Stochastic differential equations: Weak solution](https://invisiblenetwork.ai/learn/nptel/111106134/123f25d14f3d) (Video)
47. [Functional Stochastic Differential Equations](https://invisiblenetwork.ai/learn/nptel/111106134/76ed1645ed66) (Video)
48. [Statement of Dirichlet and Cauchy problems with variable coefficients elliptic operators](https://invisiblenetwork.ai/learn/nptel/111106134/43bfff74247a) (Video)
49. [Cauchy Problem with variable coefficients: Feynman-Kac formula: Part 1](https://invisiblenetwork.ai/learn/nptel/111106134/36beee151edb) (Video)
50. [Cauchy Problem with variable coefficients: Feynman-Kac formula: Part 2](https://invisiblenetwork.ai/learn/nptel/111106134/ef2f99d6d7c3) (Video)
51. [Semigroup of bounded linear operators on Banach space - Part 1](https://invisiblenetwork.ai/learn/nptel/111106134/2ca448483a8c) (Video)
52. [mod10lec52-Semigroup of bounded linear operators on Banach space part 2](https://invisiblenetwork.ai/learn/nptel/111106134/aa77fe75229c) (Video)
53. [mod10lec53-Growth property of C0 semigroup](https://invisiblenetwork.ai/learn/nptel/111106134/05570a2ea2b0) (Video)
54. [mod10lec54-Unique semigroup generated by a bounded linear operator](https://invisiblenetwork.ai/learn/nptel/111106134/161d3420120f) (Video)
55. [mod10lec55-Homogeneous initial value problem](https://invisiblenetwork.ai/learn/nptel/111106134/52c4a4a88f45) (Video)
56. [mod10lec56-Mild solution to homogeneous initial value problem](https://invisiblenetwork.ai/learn/nptel/111106134/b4efaf7f18bb) (Video)
57. [mod11lec57-Mild solution to inhomogeneous initial value problem](https://invisiblenetwork.ai/learn/nptel/111106134/799fe8fe03c2) (Video)
58. [mod11lec58-Sufficient condition for existence of classical solution of iIVP](https://invisiblenetwork.ai/learn/nptel/111106134/8b928c1aa833) (Video)
59. [mod11lec59-Tutorial on Resolvant operator](https://invisiblenetwork.ai/learn/nptel/111106134/4b6c55464ac5) (Video)
60. [mod11lec60-Feynman-Kac formula and the formula of variations of constants](https://invisiblenetwork.ai/learn/nptel/111106134/acf45b31fd97) (Video)
61. [mod11lec61-Non-autonomous evolution problem and mild/generalized solution](https://invisiblenetwork.ai/learn/nptel/111106134/d850c8ebb0c1) (Video)
62. [mod12lec62-Sufficient condition for existence of an evolution system](https://invisiblenetwork.ai/learn/nptel/111106134/f9b82bb87d0d) (Video)
63. [mod12lec63-Y-valued solution](https://invisiblenetwork.ai/learn/nptel/111106134/9b17d41f5e77) (Video)
64. [mod12lec64-mild/generalized solution to Semi-linear Evolution Problem](https://invisiblenetwork.ai/learn/nptel/111106134/e5e6f37b7ed0) (Video)
65. [mod12lec65-Existence of classical solution Part 1](https://invisiblenetwork.ai/learn/nptel/111106134/87c4b72e7ef2) (Video)
66. [mod12lec66-Existence of classical solution Part 2](https://invisiblenetwork.ai/learn/nptel/111106134/91f86de2bdfe) (Video)
67. [mod12lec67-Conclusion](https://invisiblenetwork.ai/learn/nptel/111106134/da602e695b37) (Video)