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 $1\leq p\leq \infty$ 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 Lévy processes, many questions arise from these improvements.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2019
- DOI:
- 10.48550/arXiv.1904.09565
- arXiv:
- arXiv:1904.09565
- Bibcode:
- 2019arXiv190409565K
- Keywords:
-
- Mathematics - Probability;
- Mathematics - Analysis of PDEs;
- 47A75;
- 49Q20;
- 35R11;
- 60J65;
- 60G52
- E-Print:
- 14 pages