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

Yu. E. Gliklikh

Voronezh State University

Abstract: 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.

UDC: 515.168

 English version: Journal of Mathematical Sciences (New York), 2009, 159:6, 794–798

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