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

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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.

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Authors and Affiliations

  1. Mathematics Faculty, Voronezh State University, Universitetskaya pl., 1, 394006, Voronezh, Russia

    Yu. E. Gliklikh

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  1. Yu. E. Gliklikh
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Correspondence to Yu. E. Gliklikh.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 8, pp. 69–76, 2007.

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Gliklikh, Y.E. A necessary and sufficient condition for the global-in-time existence of solutions to stochastic differential and parabolic equations on manifolds. J Math Sci 159, 794–798 (2009). https://doi.org/10.1007/s10958-009-9471-6

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  • DOI: https://doi.org/10.1007/s10958-009-9471-6

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