Symmetrization of Lévy processes and applications

2009/07/09 by Rodrigo Banuelos, Banuelos, Rodrigo, Pedro J. Mendez-Hernandez +1
Mathematics · #35J10 #47A75 #60J45 #FOS: Mathematics #Probability (math.PR) #Spectral Theory (math.SP) #math.PR #math.SP #msc:35J10 #msc:47A75 #msc:60J45

paper · pdf · doi:10.48550/arxiv.0907.1598

25 pages

arxiv created 2009/07/09 · arxiv updated 2009/12/01

Abstract

It is shown that many of the classical generalized isoperimetric inequalities for the Laplacian when viewed in terms of Brownian motion extend to a wide class of Levy processes. The results are derived from the multiple integral inequalities of Brascamp, Lieb and Luttinger but the probabilistic structure of the processes plays a crucial role in the proofs.

Related

• Brownian motion and Symmetrization
• Symmetric Rearrangements Around Infinity with Applications to Levy Processes
• Levy's distributional property for symmetric Levy processes
• Quantitative inequalities for the expected lifetime of Brownian motion
• Explicit identities for Lévy processes associated to symmetric stable processes