Modules / Lectures

Name | Download | Download Size |
---|---|---|

Lecture Note | Download as zip file | 126M |

Sl.No | Chapter Name | English |
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1 | Prerequisite Measure Theory - Part 01 | Download Verified |

2 | Prerequisite Measure Theory - Part 02 | Download Verified |

3 | Prerequisite Measure Theory - Part 03 | Download Verified |

4 | Random variable | Download Verified |

5 | Stochastic Process | Download Verified |

6 | Conditional Expectation | Download Verified |

7 | Preliminary for Stochastic Integration - Part 01 | Download Verified |

8 | Preliminary for Stochastic Integration - Part 02 | Download Verified |

9 | Definition and properties of Stochastic Integration - Part 01 | Download Verified |

10 | Definition and properties of Stochastic Integration - Part 02 | Download Verified |

11 | Further properties of Stochastic Integration | Download Verified |

12 | Extension of stochastic integral | Download Verified |

13 | change of variable formula and proof - Part 1 | Download Verified |

14 | change of variable formula and proof - Part 2 | Download Verified |

15 | Brownian motion as the building block | Download Verified |

16 | Brownian motion and its martingale property - Part 1 | Download Verified |

17 | Brownian motion and its martingale property - Part 2 | Download Verified |

18 | Application of Ito’s rule on Ito process | Download Verified |

19 | Harmonic function and its properties | Download Verified |

20 | Maximum principle of harmonic function | Download Verified |

21 | Dirichlet Problem and bounded solution | Download Verified |

22 | Example of a Dirichlet problem | Download Verified |

23 | Regular points at the boundary | Download Verified |

24 | Zarembas cone condition for regularity | Download Verified |

25 | Summary of the Zaremba's cone condition | Download Verified |

26 | Continuity of candidate solution at regular points - Part 1 | Download Verified |

27 | Continuity of candidate solution at regular points - Part 2 | Download Verified |

28 | Summary of bounded solution to the Dirichlet Problem | Download Verified |

29 | Stochastic representation of bounded solution to a heat equation - Part 1 | Download Verified |

30 | Stochastic representation of bounded solution to a heat equation - Part 2 | Download Verified |

31 | Uniqueness of solution to the heat equation | Download Verified |

32 | Remark on Tychonoff's Theorem | Download Verified |

33 | Widder’s result and its extension on heat equation | Download Verified |

34 | Solution to the mixed initial boundary value problem | Download Verified |

35 | The Feynman-Kac formula | Download Verified |

36 | Kac’s theorem on the stochastic representation of solution to a second-order linear ODE - Part 1 | Download Verified |

37 | Kac’s theorem on the stochastic representation of solution to a second-order linear ODE - Part 2 | Download Verified |

38 | Geometric Brownian motion | Download Verified |

39 | A system of stochastic differential equations in application | Download Verified |

40 | Brownian bridge | Download Verified |

41 | Simulation of stochastic differential equations | Download Verified |

42 | Stochastic differential equations: Uniqueness | Download Verified |

43 | Stochastic differential equations: Existence part 1 | Download Verified |

44 | Stochastic differential equations: Existence part 2 | Download Verified |

45 | Stochastic differential equations: Existence part 3 | Download Verified |

46 | Stochastic differential equations: Weak solution | Download Verified |

47 | Functional Stochastic Differential Equations | Download Verified |

48 | Statement of Dirichlet and Cauchy problems with variable coefficients elliptic operators | Download Verified |

49 | Cauchy Problem with variable coefficients: Feynman-Kac formula: Part 1 | Download Verified |

50 | Cauchy Problem with variable coefficients: Feynman-Kac formula: Part 2 | Download Verified |

51 | Semigroup of bounded linear operators on Banach space - Part 1 | Download Verified |

52 | Semigroup of bounded linear operators on Banach space part 2 | Download Verified |

53 | Growth property of C0 semigroup | Download Verified |

54 | Unique semigroup generated by a bounded linear operator | Download Verified |

55 | Homogeneous initial value problem | Download Verified |

56 | Mild solution to homogeneous initial value problem | Download Verified |

57 | Mild solution to inhomogeneous initial value problem | Download Verified |

58 | Sufficient condition for existence of classical solution of iIVP | Download Verified |

59 | Tutorial on Resolvant operator | Download Verified |

60 | Feynman-Kac formula and the formula of variations of constants | Download Verified |

61 | Non-autonomous evolution problem and mild/generalized solution | Download Verified |

62 | Sufficient condition for existence of an evolution system | Download Verified |

63 | Y-valued solution | Download Verified |

64 | " mild/generalized solution to Semi-linear Evolution Problem" | Download Verified |

65 | Existence of classical solution part 1 | Download Verified |

66 | Existence of classical solution part 2 | Download Verified |

67 | Conclusion video | Download Verified |

Sl.No | Language | Book link |
---|---|---|

1 | English | Download |

2 | Bengali | Not Available |

3 | Gujarati | Not Available |

4 | Hindi | Not Available |

5 | Kannada | Not Available |

6 | Malayalam | Not Available |

7 | Marathi | Not Available |

8 | Tamil | Not Available |

9 | Telugu | Not Available |