MATH0079-1 : Stochastic process

Study Programmes 2016-2017

MATH0079-1

Stochastic process

Duration :

20h Th, 10h Pr, 20h Proj.

Number of credits :

Master in mathematics (120 ECTS)		6

Lecturer :

Yvik Swan

Language(s) of instruction :

French language

Organisation and examination :

Teaching in the first semester, review in January

Units courses prerequisite and corequisite :

Prerequisite or corequisite units are presented within each program

Learning unit contents :

Introduction to stochastic processes and stochastic integration
One-dimensional Brownian Motion

Motivation
Multivariate Normal Distribution
Processes with stationary independent increments
Brownian Motion : definition
Brownian Motion : construction
An overview of path properties
Markov property and applications
Continuous time martingales and applications
Skorokhod embedding (overview)
Donsker's theorem and applications (overview)

Feller processes

Basic setup
From Feller processes to infinitesimal description
From infinitesimal description to Feller processes
A few tools
Applications to Brownian motion

Stochastic integration

Motivation
The Itô integral
Itô's formula and applications

Learning outcomes of the learning unit :

The objective is to offer the student the necessary tools to enter a very active but demanding research field.

Prerequisite knowledge and skills :

It is compulsory to have a solid background in mathematics (BA in mathematics).

The course "Introduction to Stochastic Processes" is not a pre-requisite.

Planned learning activities and teaching methods :

Ex cathedra classes as well as exercise sessions

Mode of delivery (face-to-face ; distance-learning) :

Face-to-face