Probabilistic Methods in PDE KEXCR4T6ZN

URI	`m2://res/KEXCR4T6ZN`
Kind	course
Creators	Anindya Goswami (instructor)
Date	2020-01-26
Scope	in

Expressions

e1: edition

Language	en
Date	2020-01-26

m1: page, IISER Pune (record). nptel 111106134
m2: page, 2020-01-26 (record). nptel 111106134

Contents

part 1: week-01
session 1: Prerequisite Measure Theory - Part 01
session 2: Prerequisite Measure Theory - Part 02
session 3: Prerequisite Measure Theory - Part 03
session 4: Random variable
session 5: Stochastic Process
session 6: Conditional Expectation
part 2: week-02
session 7: Preliminary for Stochastic Integration - Part 01
session 8: Preliminary for Stochastic Integration - Part 02
session 9: Definition and properties of Stochastic Integration - Part 01
session 10: Definition and properties of Stochastic Integration - Part 02
session 11: Further properties of Stochastic Integration
part 3: week-03
session 12: Extension of stochastic integral
session 13: change of variable formula and proof - Part 1
session 14: change of variable formula and proof - Part 2
session 15: Brownian motion as the building block
session 16: Brownian motion and its martingale property - Part 1
session 17: Brownian motion and its martingale property - Part 2
part 4: week-04
session 18: Application of Itoâ€™s rule on Ito process
session 19: Harmonic function and its properties
session 20: Maximum principle of harmonic function
session 21: Dirichlet Problem and bounded solution
session 22: Example of a Dirichlet problem
session 23: Regular points at the boundary
session 24: Zarembas cone condition for regularity
part 5: week-05
session 25: Summary of the Zaremba's cone condition
session 26: Continuity of candidate solution at regular points - Part 1
session 27: Continuity of candidate solution at regular points - Part 2
session 28: Summary of bounded solution to the Dirichlet Problem
session 29: Stochastic representation of bounded solution to a heat equation - Part 1
session 30: Stochastic representation of bounded solution to a heat equation - Part 2
part 6: week-06
session 31: Uniqueness of solution to the heat equationÂ
session 32: Remark on Tychonoff's Theorem
session 33: Widderâ€™s result and its extension on heat equation
session 34: Solution to the mixed initial boundary value problemÂ
session 35: The Feynman-Kac formulaÂ
part 7: week-07
session 36: Kacâ€™s theorem on the stochastic representation of solution to a second-order linear ODE - Part 1
session 37: Kacâ€™s theorem on the stochastic representation of solution to a second-order linear ODE - Part 2
session 38: Geometric Brownian motion
session 39: A system of stochastic differential equations in application
session 40: Brownian bridge
part 8: week-08
session 41: Simulation of stochastic differential equations
session 42: Stochastic differential equations: Uniqueness
session 43: Stochastic differential equations: Existence part 1
session 44: Stochastic differential equations: Existence part 2
session 45: Stochastic differential equations: Existence part 3
session 46: Stochastic differential equations: Weak solution
part 9: week-09
session 47: Functional Stochastic Differential Equations
session 48: Statement of Dirichlet and Cauchy problems with variable coefficients elliptic operators
session 49: Cauchy Problem with variable coefficients: Feynman-Kac formula: Part 1
session 50: Cauchy Problem with variable coefficients: Feynman-Kac formula: Part 2
session 51: Semigroup of bounded linear operators on Banach space - Part 1
part 10: week-10
session 52: mod10lec52-Semigroup of bounded linear operators on Banach space part 2
session 53: mod10lec53-Growth property of C0 semigroup
session 54: mod10lec54-Unique semigroup generated by a bounded linear operator
session 55: mod10lec55-Homogeneous initial value problem
session 56: mod10lec56-Mild solution to homogeneous initial value problem
part 11: week-11
session 57: mod11lec57-Mild solution to inhomogeneous initial value problem
session 58: mod11lec58-Sufficient condition for existence of classical solution of iIVP
session 59: mod11lec59-Tutorial on Resolvant operator
session 60: mod11lec60-Feynman-Kac formula and the formula of variations of constants
session 61: mod11lec61-Non-autonomous evolution problem and mild/generalized solution
part 12: week-12
session 62: mod12lec62-Sufficient condition for existence of an evolution system
session 63: mod12lec63-Y-valued solution
session 64: mod12lec64-mild/generalized solution to Semi-linear Evolution Problem
session 65: mod12lec65-Existence of classical solution Part 1
session 66: mod12lec66-Existence of classical solution Part 2
session 67: mod12lec67-Conclusion

Catalogue records

nptel: 111106134 (manifestation)
nptel_video: 111106134 (manifestation)