Stochastic PDE

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Keywords

Stochastic PDE

Objectives

This course will introduce the notion of stochastic process and Itô’s integral. Then, some stochastic differential equations and their applications to PDE will be studied. In parallel, this course will come back on the standard techniques for monotone PDE to think of an application to stochastic PDE.

 

Number of hours

  • CM : 27
  • TD : 12

Form of assessment

First session

Second session

Final examination: 100%

Final examination length: 3 hours

Remedial examination: 100 %

Remedial examination length: 3 hours

Syllabus

I. Advanced probability: probability space, random variables, processes, filtrations, Brownian motion, and martingales.

II. Itô calculus: Itô integral (construction et properties), Itô formula

III. Stochastic differential equations in finite dimensional spaces: examples, existence and uniqueness.

Applications to PDE:

IV. Stochastic differential equations in infinite dimensional spaces: some stochastic PDE

V. Discretisation and simulations of the trajectories of the solution to stochastic differential equations. 

Bibliography:

Dautray Lions : Analyse mathématique et calcul numérique.

Brézis : Functional analysis.

Evans : Partial Differential Equations.

Oksendal : Stochastic Differential Equations.

Billingsley : Probability and measure

In brief

ECTS credits 4

Number of hours 39

Level of study Master degree level

Contact(s)

Organizational unit

Person in charge(s)

Vallet Guy

Email : guy.vallet @ univ-pau.fr

Puig Bénédicte

Email : benedicte.puig @ univ-pau.fr

Administrative contact(s)

Secrétariat de Mathématiques - Brigitte GAUBERT

Email : brigitte.gaubert @ univ-pau.fr

Places

  • Pau