Quantitative inequalities for the expected lifetime of Brownian motion

2019/04/21 by Daesung Kim, Kim, Daesung · 3 citations
Mathematics · #35R11 #47A75 #49Q20 #60G52 #60J65 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #math.AP #math.PR #msc:35R11 #msc:47A75 #msc:49Q20 #msc:60G52 #msc:60J65

paper · pdf · doi:10.48550/arxiv.1904.09565

14 pages

arxiv created 2019/04/21 · arxiv updated 2019/04/23

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≤ p≤ ∞ 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.

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