## Stochastic geometric wave equations with values in compact Riemannian homogeneous spaces

Research output: Contribution to journalArticlepeer-review

## Department/unit(s)

### Publication details

Journal Annals of Probability Published - May 2013 3B 41 44 1938-1977 English

### 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.

### Research areas

• stochastic wave equation, , Riemannian manifold, , homogeneous space.

• ## Some questions related to invariant measures for stochastic Navier Stokes equations

Project: Research project (funded)Research

• ## Award for Best Paper 2013, 1st prize, Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic

Prize: Prize (including medals and awards)

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