Exit Time Moments and Eigenvalue Estimates

Abstract

We study estimates involving the principal Dirichlet eigenvalue associated to a smoothly bounded domain in a complete Riemannian manifold and L1-norms of exit time moments of Brownian motion. Our results generalize a classical inequality of Polya.

15 pages, added appendix on variational quotients, added lower bounds, improved exposition

Cited by in corpus (4)

• Bounds for exit times of Brownian motion and the first Dirichlet eigenvalue for the Laplacian
• Comparison Results, Exit Time Moments, And Eigenvalues On Riemannian Manifolds With A Lower Ricci Curvature Bound
• Variational principles for the exit time of non-symmetric diffusions
• Spectral bounds for exit times on metric measure Dirichlet spaces and applications