Sumários

Stochastic Differential Equations

29 Setembro 2025, 12:00 • João Guerra

Stochastic Differential Equations: the Ornstein-Uhlenbeck process with mean reversion. 

Discussion of exercises on the application of Ito formula and stochastic differential equations.

Stochastic Differential Equations

23 Setembro 2025, 11:30 • João Guerra

Discussions of exercises on the application of Ito formula. 

Ordinary differential equations and stochastic differential equations: introduction, definition of solution. 
Examples of solvable stochastic differential equations: the geometric Brownian motion SDE and the Ornstein-Uhlenbeck or Langevin SDE. 

Ito processes and Ito formula

22 Setembro 2025, 12:00 • João Guerra

Ito processes: definition and examples. 

One dimensional Ito formula: examples and exercises. 
Multidimensional Brownian motion, multidimensional Ito processes and multidimensional Ito formula: examples and exercises. 

Stochastic integrals of adapted processes and One-dimensional Itô formula

16 Setembro 2025, 11:30 • João Guerra

Stochastic integrals of adapted processes of class L^2,a,T. Definition and basic properties. 

Example of calculation of a stochastic integral of adapted process by definition. 
Equality dB^2 = dt and the one-dimensional Itô formula as a stochastic chain rule. 
Simple example of application of Itô formula. 

Stochastic integral

15 Setembro 2025, 12:00 • João Guerra

Discussion of exercises on martingales.

Motivation for the definition of stochastic integral. 
Simples processes. Definition and examples. 
Stochastic integral for simple processes: definition and examples.