Sumários

Stochastic Differential Equations - continuation

11 Abril 2024, 11:00 • João Guerra

Theorem of existence and uniqueness of solutions for stochastic differential equations. 

The linear growth condition and the Lipschitz property: examples. 
Discussion of exercises on the application of the Itô formula and on stochastic differential equations.

Stochastic Differential Equations - Introduction

9 Abril 2024, 11:30 • João Guerra

Introduction to Stochastic Differential Equations. 

Examples: Geometric Brownian motion SDE, Ornstein-Uhlenbeck or Langevin SDE. 
The Mean-reversion Ornstein-Uhlenbeck process SDE. 

Aula substituida em 22-04-2024 - Systems of linear SDE's and exta topics on SDE's

2 Abril 2024, 11:30 • João Guerra

Systems of linear SDE's: matrix exponential and general solution of a system of linear SDE's. Example. 

Diffusion processes as Markov processes: the transition probabilities and the transition probability density function. Examples. 
The Stratonovich stochastic integral and Stratonovich SDE's and its relationship with the Ito stochastic integral and Ito SDE's. Examples. 

Exercises

21 Março 2024, 11:00 • João Guerra

Discussion of exercises about Itô formula, its applications, the Itô representation theorem and the martingale representation theorem. 

Ito representation Theorem and Martingale representation Theorem

19 Março 2024, 11:30 • João Guerra

Itô representation Theorem and martingale representation Theorem. 

Examples.
An integration by parts formula. 
Discussion of exercises about the application of the Itô formula.