FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2007, VOLUME 13, NUMBER 8, PAGES 69-76

A necessary and sufficient condition for the global-in-time existence of solutions to stochastic differential and parabolic equations on manifolds

Yu. E. Gliklikh

Abstract

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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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Last modified: June 13, 2008