Brownian Motion and Harmonic Functions on Rotationally Symmetric Manifolds
March, Peter
Ann. Probab., Tome 14 (1986) no. 4, p. 793-801 / Harvested from Project Euclid
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We consider Brownian motion $X$ on a rotationally symmetric manifold $M_g = (\mathbb{R}^n, ds^2), ds^2 = dr^2 + g(r)^2 d\theta^2$. An integral test is presented which gives a necessary and sufficient condition for the nontriviality of the invariant $\sigma$-field of $X$, hence for the existence of nonconstant bounded harmonic functions on $M_g$. Conditions on the sectional curvatures are given which imply the convergence or the divergence of the test integral.
Publié le : 1986-07-14
Classification:  Skew product,  invariant $\sigma$-field,  sectional curvature,  60G65,  58G32 
@article{1176992438,
     author = {March, Peter},
     title = {Brownian Motion and Harmonic Functions on Rotationally Symmetric Manifolds},
     journal = {Ann. Probab.},
     volume = {14},
     number = {4},
     year = {1986},
     pages = { 793-801},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176992438}
}

March, Peter. Brownian Motion and Harmonic Functions on Rotationally Symmetric Manifolds. Ann. Probab., Tome 14 (1986) no. 4, pp.  793-801. http://gdmltest.u-ga.fr/item/1176992438/