Feynman-Kac formulas for parabolic PDE's with boundary condition

6 Maio 2019, 10:00 • João Guerra

Stochastic representation formulas for solutions of parabolic PDE's with boundary conditions. 

Feynman-Kac formulas. 

Exercises. 

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Diffusion processes as Markov processes and Discussion of Exercises

29 Abril 2019, 10:00 • João Guerra

Diffusion processes as Markov processes. The transition probabilities for solutions of Stochastic Differential Equations. Example. 

Discussion of Exercises on Stochastic Differential Equations and applications of Itô formula. 

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Numerical methods for stochastic differential equations

24 Abril 2019, 12:30 • João Guerra

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

The error estimates.  

Example. 

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Stochastic Differential Equations

10 Abril 2019, 12:30 • João Guerra

Existence and Uniqueness Theorem for stochastic differential equations in dimension one. Example.

Linear and semi-linear stochastic differential equations. Examples.

 

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Existence and uniqueness Theorem for SDE's

8 Abril 2019, 10:00 • João Guerra

Ornstein-Uhlenbeck process with mean reversion. Solution of the SDE. Stationary and Invariant distribution. 

Existence and Uniqueness Theorem. Proof by the fixed point theorem. 

Examples of application of the Theorem and examples where the theorem cannot be applied. 

 

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