Stochastic geometric wave equations with values in compact Riemannian homogeneous spaces

By Zdzisław Brzeźniak, Martin Ondrej'at. 2011

71 citations recorded by the source corpus.

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.

Subfields: Control and Systems Engineering, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c3f17569d150924b23067c4863e59af67b7d412d

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In Control and Systems Engineering

1. El.zbieta Motyl
2. Zdzisław Brzeźniak
3. Bixiang Wang
4. Wei Liu

In Finance

1. El.zbieta Motyl
2. Zdzisław Brzeźniak
3. J. V. Neerven
4. Lutz Weis
5. Bixiang Wang
6. Wei Liu
7. Mark Veraar

In Mathematical Physics

1. El.zbieta Motyl
2. Zdzisław Brzeźniak
3. J. V. Neerven

Citations in the corpus

• Stochastic Navier–Stokes Equations Driven by Lévy Noise in Unbounded 3D Domains (2012, methodology): “Let us recall the following Jakubowski’s version of the Skorokhod Theorem [18], see also Brzeźniak and Ondreját [10].”
• Existence of a martingale solution of the stochastic Navier-Stokes equations in unbounded 2D and 3D-domains (2012, methodology): “1 in [11]) Let X be a topological space such that there exists a sequence {fm} of continuous functions fm : X → R that separates points of X .”