Quantitative inequalities for the expected lifetime of Brownian motion

Abstract

The isoperimetric inequalities for the expected lifetime of Brownian motion state that the $L^p$-norms of the expected lifetime in a bounded domain for $1\le p\le \infty$ are maximized when the region is a ball with the same volume. In this paper, we prove quantitative improvements of the inequalities. Since the isoperimetric properties hold for a wide class of Lévy processes, many questions arise from these improvements.

14 pages

References in corpus (2)

• A sharpened Hausdorff-Young inequality
• Eigenvalue gaps for the Cauchy process and a Poincaré inequality

Cited by in corpus (1)

• Maximizing the $p$-th moment of exit time of planar Brownian motion from a given domain