Radial Part of Brownian Motion on a Riemannian Manifold
Liao, M. ; Zheng, W. A.
Ann. Probab., Tome 23 (1995) no. 3, p. 173-177 / Harvested from Project Euclid
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Let $\rho_t$ be the radial part of a Brownian motion in an $n$-dimensional Riemannian manifold $M$ starting at $x$ and let $T = T_\varepsilon$ be the first time $t$ when $\rho_t = \varepsilon$. We show that $E\lbrack \rho^2_{t\wedge T} \rbrack = nt - (1/6)S(x)t^2 + \sigma(t^2)$, as $t \downarrow 0$, where $S(x)$ is the scalar curvature. The same formula holds for $E\lbrack\rho^2_t\rbrack$ under some boundedness condition on $M$.
Publié le : 1995-01-14
Classification:  Brownian motion,  Riemannian manifolds,  58G32,  60J65 
@article{1176988382,
     author = {Liao, M. and Zheng, W. A.},
     title = {Radial Part of Brownian Motion on a Riemannian Manifold},
     journal = {Ann. Probab.},
     volume = {23},
     number = {3},
     year = {1995},
     pages = { 173-177},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176988382}
}

Liao, M.; Zheng, W. A. Radial Part of Brownian Motion on a Riemannian Manifold. Ann. Probab., Tome 23 (1995) no. 3, pp.  173-177. http://gdmltest.u-ga.fr/item/1176988382/