STOCHASTIC GEOMETRIC WAVE EQUATIONS WITH VALUES IN COMPACT RIEMANNIAN HOMOGENEOUS SPACES
成果类型：
Article
署名作者：
Brzezniak, Zdzislaw; Ondrejat, Martin
署名单位：
University of York - UK; Czech Academy of Sciences; Institute of Information Theory & Automation of the Czech Academy of Sciences
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/11-AOP690
发表日期：
2013
页码：
1938-1977
关键词：
weak solutions
cauchy-problem
HARMONIC MAPS
evolution-equations
spdes driven
martingale
EXISTENCE
SINGULARITIES
smoothness
REGULARITY
摘要：
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 D-t partial derivative(t)u = Sigma(d)(k=1) D-xk partial derivative(xk)u+f(u)(Du)+g(u)(D-u)(W) over dot in any dimension d >= 1, where f and g are continuous multilinear maps, and W is a spatially homogeneous Wiener process on 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.
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