The Kolmogorov Equations. Exercises

3 Maio 2018, 10:00 • João Guerra

The Kolmogorov Equations: the backward equation and the forward equation (the Fokker-Planck Equation). Examples. 

Discussion of exercises about the application of Feynman-Kac formulas. 

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Solutions of SDE's, Diffusions, PDE's and Feynman-Kac formulas

30 Abril 2018, 10:00 • João Guerra

Diffusions as Markov processes. 

The transition probabilities for diffusions. Examples. 

Parabolica PDE's, Diffusions as solutions of SDE's and the Feynman-Kac formulas for stochastic representation of the solutions of certain parabolic PDE's. Examples. 

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Exercises

26 Abril 2018, 10:00 • João Guerra

Exercises on applications of Itô formula and stochastic differential equations. 

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Linear Stochastic Differential Equations. Numerical Methods

23 Abril 2018, 10:00 • João Guerra

Linear stochastic differential equations. How to solve them using an integrating factor and process separation. 

Example. 

Numerical methods for stochastic differential equations: the Euler Scheme and the Millstein Scheme. 

Order of convergence of the schemes. 

Algorithms for simulating the numerical solutions of SDE's.

 

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Existence and uniqueness theorem for SDE's

19 Abril 2018, 10:00 • João Guerra

Existence and Uniqueness theorem for solutions of stochastic differential equations: proof using the fixed point theorem. 

Example of a deterministic differential equation which has a solution that "explodes" in finite time. 

Examples of functions which have linear growth and are Lipschitz and functions which are not. 

 

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