Stochastic differential equations on noncompact manifolds: Moment stability and its topological consequences

DOI10.1007/BF01268987zbMath0815.60049arXiv1911.07900OpenAlexW2067551839MaRDI QIDQ1343613

Xue-Mei Li

Publication date: 30 June 1995

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.07900

zbMATH Keywords

Riemannian manifoldRicci curvaturestochastic dynamical systemsrecurrence propertyBrownian system with driftexplosion time of the solution

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Applications of stochastic analysis (to PDEs, etc.) (60H30) Diffusion processes and stochastic analysis on manifolds (58J65) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (11)

A universal, canonical dispersive ordering in metric spaces ⋮ Estimates for the volume variation of compact submanifolds driven by a stochastic flow ⋮ Strong \(p\)-completeness of stochastic differential equations and the existence of smooth flows on noncompact manifolds ⋮ Admissible vector fields and related diffusions on infinite-dimensional manifolds ⋮ Incompressible Euler equations with stochastic forcing: a geometric approach ⋮ On the differentiation of heat semigroups and poisson integrals ⋮ Contractibility of manifolds by means of stochastic flows ⋮ Heat equation derivative formulas for vector bundles ⋮ A Poincaré inequality on loop spaces ⋮ Heat flow regularity, Bismut-Elworthy-Li's derivative formula, and pathwise couplings on Riemannian manifolds with Kato bounded Ricci curvature ⋮ A new definition of rough paths on manifolds

Cites Work

• Generalized Bochner theorems and the spectrum of complete manifolds
• Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
• Homotopy and homology vanishing theorems and the stability of stochastic flows
• Stochastic flows of diffeomorphisms on an open set in rⁿ
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