Sumários

Feynman-Kac formula and exercises

28 Abril 2022, 13:30 • João Guerra

Feynman-Kac formulas.

Derivation and discussion of exercises.

Inifinitesimal generators and Feynman-Kac formula

22 Abril 2022, 10:00 • João Guerra

Infinitesimal generators of diffusions. Examples. 

A Feynman-Kac formula for PDE's - stochastic representation of solutions of PDE's. Example. 

Markov property of diffusions and Stratonovich SDE's

21 Abril 2022, 13:30 • João Guerra

Markov property of diffusions (solutions of stochastic differential equations). Transition probabilities for Markov processes and for diffusions. Examples. 


Stratonovich integral and Stratonovich SDE's. Transform Stratonovich SDE's into Ito SDE's. Example. 

Exercises.

Stochastic differential equations: numerical approximations

8 Abril 2022, 10:00 • João Guerra

Existence and uniqueness theorem for one-dimensional SDE's. 

Weak solutions of SDE's - brief introduction. 
Numerical approximations of solutions of SDE's: the Euler scheme and the Millstein scheme. 
Discussion of an exercise on SDE's. 

Linear stochastic Differential Equations

7 Abril 2022, 13:30 • João Guerra

Ornstein-Uhlenbeck process with mean reversion SDE and applications to finance. 
Stochastic differential equations with nonlinear drift: a solution method.
Linear stochastic Differential Equations: methods of solution. 
Discussion of exercises on stochastic differential equations.