Stochastic partial
differential equations

This is a  homepage dedicated to stochastic partial differential equations (SPDEs) and their applications. 
I maintain this website in my spare time, so dont be offended if your latest paper is not listed! Be kind and send me an e-mail.


Introduction/ Scientific events /
Applications of SPDEs
People / Books / Research articles.


A stochastic partial differential equation (SPDE) is a partial differential equation containing a random (noise) term. The study of SPDEs is an exciting topic which brings together techniques from probability theory, functional analysis, and the theory of partial differential equations.

Stochastic partial differential equations appear in several different applications: study of random evolution of systems with a spatial extension (random interface growth, random evolution of surfaces, fluids subject to random forcing), study of stochastic models where the state variable is infinite dimensional (for example, a curve or surface).

The solution to a stochastic partial differential equations may be viewed in several manners. One can view a solution as a random field (set of random variables indexed by a multidimensional parameter). In the case where the SPDE is an evolution equation, the infinite dimensional point of view consists in viewing the solution at a given time as a random element in a function space and thus view the SPDE as a stochastic evolution equation in an infinite dimensional space. In the pathwise point of view, tries to give a meaning to the solution for (almost) every realization of the noise and then view the solution as a random variable on the set of (infinite dimensional) paths thus defined.


Centre de Mathématiques Appliquées
CNRS - Ecole Polytechnique
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