Sumários

1 Abril 2025, 11:30 • João Guerra

Changes of measure. Density for the change of measure.

Example with a normal random variable.

The Girsanov theorem for the Brownian motion. The likelihood process. Example.

The general Girsanov theorem in dimension oe. Example.

27 Março 2025, 11:00 • João Guerra

The Kolmogorov Backward operator and the Kolmogorov Backward Equation.

The Kolmogorov Forward Equation or Fokker-Planck Equation. Examples.

Discussion of exercises on PDE's and SDE's.

25 Março 2025, 11:30 • João Guerra

Feynman-Kac formulas.

Markov property for diffusions.

Transition probabilities. Examples.

Discussion of exercises on PDE's and stochastic differential equations.

20 Março 2025, 11:00 • João Guerra

Feynman-Kac formulas.

Examples.

Discussion of exercises about Stochastic Differential Equations.

18 Março 2025, 11:30 • João Guerra

Infinitesimal generator of a diffusion. Definition and examples.

PArabolic PDE's and a stochastic representation formula for the solution: the Feynman-Kac formula.

Example.

Discussion of exercises on Stochastic Differential Equations.