Geodesic
A necessary and sufficient condition for the global-in-time existence of solutions to stochastic differential and parabolic equations on manifolds
Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 8, pp. 69-76 
Yu. E. Gliklikh. A necessary and sufficient condition for the global-in-time existence of solutions to stochastic differential and parabolic equations on manifolds. Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 8, pp. 69-76. http://geodesic.mathdoc.fr/item/FPM_2007_13_8_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A necessary and sufficient condition of one-sided type for the completeness of a stochastic flow and the corresponding diffusion semigroup on a manifold $M$ is found under the assumption that the space $C_0(M)$ of functions is invariant.

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