Projects per year
Abstract
Let $M$ be a compact Riemannian homogeneous space (e.g. a Euclidean sphere). We prove existence of a global weak solution of the stochastic wave equation \mathbf D_t\partial_tu=\sum_{k=1}^d\mathbf D_{x_k}\partial_{x_k}u+f_u(Du)+g_u(Du)\,\dot W$ in any dimension $d\ge 1$, where $f$ and $g$ are continuous multilinear mappings and $W$ is a spatially homogeneous Wiener process on $\mathbb R^d$ with finite spectral measure. A nonstandard method of constructing weak solutions of SPDEs, that does not rely on martingale representation theorem, is employed.
Original language  English 

Pages (fromto)  19381977 
Number of pages  44 
Journal  Annals of Probability 
Volume  41 
Issue number  3B 
DOIs  
Publication status  Published  May 2013 
Keywords
 stochastic wave equation,
 Riemannian manifold,
 homogeneous space.
Projects
 1 Finished

Some questions related to invariant measures for stochastic Navier Stokes equations
29/11/06 → 28/04/09
Project: Research project (funded) › Research