Proceedings of the Korean Statistical Society Conference (한국통계학회:학술대회논문집)
- 2003.05a
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- Pages.37-42
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- 2003
THE EXPANSION OF MEAN DISTANCE OF BROWNIAN MOTION ON RIEMANNIAN MANIFOLD
- Kim, Yoon-Tae (Department of Statistics, Hallym University) ;
- Park, Hyun-Suk (Department of Statistics, Hallym University) ;
- Jeon, Jong-Woo (Department of Statistics, Seoul National University)
- Published : 2003.05.23
Abstract
We study the asymptotic expansion in small time of the mean distance of Brownian motion on Riemannian manifolds. We compute the first four terms of the asymptotic expansion of the mean distance by using the decomposition of Laplacian into homogeneous components. This expansion can he expressed in terms of the scalar valued curvature invariants of order 2, 4, 6.
Keywords
- Brownian motion;
- Riemannian manifold;
- Curvature invariants;
- Ricci curvature;
- Scalar curvature;
- Bianchi's identity;
- Ricci's identity