Stochastic geometric wave equations with values in compact Riemannian homogeneous spaces

• Zdzisław Brzeźniak ^[1] ; Martin Ondreját ^[2]
  1. [1] University of York

     University of York

     Reino Unido

     
  2. [2] Institute of Informatioin Theory and Automation of the ASCR
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 41, Nº. 3, 2, 2013, págs. 1938-1977
• Idioma: inglés
• DOI: 10.1214/11-AOP690
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• Resumen

  • 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 Dt∂tu=∑dk=1Dxk∂xku+fu(Du)+gu(Du)W˙ in any dimension d≥1, where f and g are continuous multilinear maps, and W is a spatially homogeneous Wiener process on Rd with finite spectral measure. A nonstandard method of constructing weak solutions of SPDEs, that does not rely on martingale representation theorem, is employed.