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

DOI10.1007/s10958-009-9471-6zbMath1183.58022OpenAlexW2113055820MaRDI QIDQ843622

Yuri E. Gliklikh

Publication date: 15 January 2010

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-009-9471-6

zbMATH Keywords

manifoldstochastic differential equationparabolic equationstochastic flow

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Diffusion processes and stochastic analysis on manifolds (58J65) Initial value problems for second-order parabolic equations (35K15) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Cites Work

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• Processus de Markov et desintégrations régulières
• Properties at infinity of diffusion semigroups and stochastic flows via weak uniform covers
• Conditions for global existence of solutions of ordinary differential, stochastic differential, and parabolic equations
• Stochastic flows and the C₀-diffusion property
• Behavior of diffusion semi-groups at infinity

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