On conservation of probability and the Feller property

DOI10.1214/aop/1042644717zbMath0854.60080OpenAlexW2030368421WikidataQ124852631 ScholiaQ124852631MaRDI QIDQ1922077

Zhongmin Qian

Publication date: 5 January 1997

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1042644717

zbMATH Keywords

diffusioncomparison theoremconservationFeller propertymodified Ricci curvature

Mathematics Subject Classification ID

Diffusion processes (60J60) Diffusion processes and stochastic analysis on manifolds (58J65)

Related Items (13)

On a classification theorem for self–shrinkers ⋮ Souplet–Zhang and Hamilton‐type gradient estimates for non‐linear elliptic equations on smooth metric measure spaces ⋮ New Laplacian comparison theorem and its applications to diffusion processes on Riemannian manifolds ⋮ Intrinsic and extrinsic comparison results for isoperimetric quotients and capacities in weighted manifolds ⋮ Liouville theorem for \(V\)-harmonic maps under non-negative \((m, V)\)-Ricci curvature for non-positive \(m\) ⋮ On generalized Schrödinger semigroups ⋮ Rigidity results and topology at infinity of translating solitons of the mean curvature flow ⋮ Spectral and stochastic properties of the \(f\)-Laplacian, solutions of PDEs at infinity and geometric applications ⋮ Space-time Wasserstein controls and Bakry-Ledoux type gradient estimates ⋮ \(L\)-harmonic functions with polynomial growth of a fixed rate ⋮ The Feller property on Riemannian manifolds ⋮ SOME GEOMETRIC ANALYSIS ON GENERIC RICCI SOLITONS ⋮ Liouville theorems for symmetric diffusion operators on complete Riemannian manifolds

Cites Work

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• Function theory on manifolds which possess a pole
• Heat semigroup on a complete Riemannian manifold
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• On the heat kernel of a complete Riemannian manifold
• Large deviation property for Riemannian Brownian motion on a complete manifold
• Heat kernel bounds, conservation of probability and the Feller property
• Strong \(p\)-completeness of stochastic differential equations and the existence of smooth flows on noncompact manifolds
• The conservation property of the heat equation on riemannian manifolds
• Explosion Problems for Symmetric Diffusion Processes
• Stochastic flows and the C₀-diffusion property
• On the Conservativeness of the Brownian Motion on a Riemannian Manifold
• Behavior of diffusion semi-groups at infinity

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