| Name | Download | Download Size |
|---|---|---|
| Lecture Note | Download as zip file | 126M |
| Sl.No | Chapter Name | MP4 Download |
|---|---|---|
| 1 | Prerequisite Measure Theory - Part 01 | Download |
| 2 | Prerequisite Measure Theory - Part 02 | Download |
| 3 | Prerequisite Measure Theory - Part 03 | Download |
| 4 | Random variable | Download |
| 5 | Stochastic Process | Download |
| 6 | Conditional Expectation | Download |
| 7 | Preliminary for Stochastic Integration - Part 01 | Download |
| 8 | Preliminary for Stochastic Integration - Part 02 | Download |
| 9 | Definition and properties of Stochastic Integration - Part 01 | Download |
| 10 | Definition and properties of Stochastic Integration - Part 02 | Download |
| 11 | Further properties of Stochastic Integration | Download |
| 12 | Extension of stochastic integral | Download |
| 13 | change of variable formula and proof - Part 1 | Download |
| 14 | change of variable formula and proof - Part 2 | Download |
| 15 | Brownian motion as the building block | Download |
| 16 | Brownian motion and its martingale property - Part 1 | Download |
| 17 | Brownian motion and its martingale property - Part 2 | Download |
| 18 | Application of Ito’s rule on Ito process | Download |
| 19 | Harmonic function and its properties | Download |
| 20 | Maximum principle of harmonic function | Download |
| 21 | Dirichlet Problem and bounded solution | Download |
| 22 | Example of a Dirichlet problem | Download |
| 23 | Regular points at the boundary | Download |
| 24 | Zarembas cone condition for regularity | Download |
| 25 | Summary of the Zaremba's cone condition | Download |
| 26 | Continuity of candidate solution at regular points - Part 1 | Download |
| 27 | Continuity of candidate solution at regular points - Part 2 | Download |
| 28 | Summary of bounded solution to the Dirichlet Problem | Download |
| 29 | Stochastic representation of bounded solution to a heat equation - Part 1 | Download |
| 30 | Stochastic representation of bounded solution to a heat equation - Part 2 | Download |
| 31 | Uniqueness of solution to the heat equation | Download |
| 32 | Remark on Tychonoff's Theorem | Download |
| 33 | Widder’s result and its extension on heat equation | Download |
| 34 | Solution to the mixed initial boundary value problem | Download |
| 35 | The Feynman-Kac formula | Download |
| 36 | Kac’s theorem on the stochastic representation of solution to a second-order linear ODE - Part 1 | Download |
| 37 | Kac’s theorem on the stochastic representation of solution to a second-order linear ODE - Part 2 | Download |
| 38 | Geometric Brownian motion | Download |
| 39 | A system of stochastic differential equations in application | Download |
| 40 | Brownian bridge | Download |
| 41 | Simulation of stochastic differential equations | Download |
| 42 | Stochastic differential equations: Uniqueness | Download |
| 43 | Stochastic differential equations: Existence part 1 | Download |
| 44 | Stochastic differential equations: Existence part 2 | Download |
| 45 | Stochastic differential equations: Existence part 3 | Download |
| 46 | Stochastic differential equations: Weak solution | Download |
| 47 | Functional Stochastic Differential Equations | Download |
| 48 | Statement of Dirichlet and Cauchy problems with variable coefficients elliptic operators | Download |
| 49 | Cauchy Problem with variable coefficients: Feynman-Kac formula: Part 1 | Download |
| 50 | Cauchy Problem with variable coefficients: Feynman-Kac formula: Part 2 | Download |
| 51 | Semigroup of bounded linear operators on Banach space - Part 1 | Download |
| 52 | Semigroup of bounded linear operators on Banach space part 2 | Download |
| 53 | Growth property of C0 semigroup | Download |
| 54 | Unique semigroup generated by a bounded linear operator | Download |
| 55 | Homogeneous initial value problem | Download |
| 56 | Mild solution to homogeneous initial value problem | Download |
| 57 | Mild solution to inhomogeneous initial value problem | Download |
| 58 | Sufficient condition for existence of classical solution of iIVP | Download |
| 59 | Tutorial on Resolvant operator | Download |
| 60 | Feynman-Kac formula and the formula of variations of constants | Download |
| 61 | Non-autonomous evolution problem and mild/generalized solution | Download |
| 62 | Sufficient condition for existence of an evolution system | Download |
| 63 | Y-valued solution | Download |
| 64 | " mild/generalized solution to Semi-linear Evolution Problem" | Download |
| 65 | Existence of classical solution part 1 | Download |
| 66 | Existence of classical solution part 2 | Download |
| 67 | Conclusion video | Download |
| Sl.No | Chapter Name | English |
|---|---|---|
| 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 |