Stochastic differential equations
Optional course 4 credits.
Theory + Exercises: 4 credits
I. Overview
This course provides :
- Brownian motions.
- Stochastic calculus and Stochastic differential equations..
II. Prerequisites
Analysis 1, 2, 3, Probability and statistic, Differential equations.
III. Contents
Chapter 1. Basic probabilty theory.
1.1 . Random variables, distribution functions, density.
1.2 Independence of Random variables.
1.3. Conditional expectation E(X |Y).
Chapter 2. Stochastic processes
2.1. Stochastic processes.
2.2. Wiener processes (Brownian motions).
2.3. Ito integral, Ito formular.
Chapter 3. Stochastic differential equations.
3.1. Solutions of stochastic differential equations.
3.2. Properties of solutions of stochastic differential equations
3.3. Modelling with stochastic differential equations.
References