Quantitative inequalities for the expected lifetime of Brownian motion

Daesung Kim

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arXiv · 1904.09565

Quantitative inequalities for the expected lifetime of Brownian motion

Daesung Kim

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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 $1\leq p\leq \infty$ 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 L\'evy processes, many questions arise from these improvements.

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Daesung Kim. 2019-04-21. Quantitative inequalities for the expected lifetime of Brownian motion. https://arxiv.org/abs/1904.09565

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