Powers of Brownian Green Potentials

Claude Dellacherie, Mauricio Duarte, Servet Martínez, Jaime San Martín, Pierre Vandaele

Research output: Contribution to journalArticlepeer-review


In this article we study stability properties of gO, the standard Green kernel for O an open regular set in ℝd. In d ≥ 3 we show that gOβ is again a Green kernel of a Markov Feller process, for any power β ∈ [1,d/(d − 2)). In dimension d = 2, we show the same result for gOβ, for any β ≥ 1 and for kernels exp(αgO),exp(αgO)−1, for α ∈ (0,2π), when O is an open Greenian regular set whose complement contains a ball.

Original languageEnglish
Pages (from-to)227-265
Number of pages39
JournalPotential Analysis
Issue number2
Early online date23 Jan 2021
Publication statusE-pub ahead of print - 23 Jan 2021


  • Brownian motion
  • Green potentials
  • Markov processes

ASJC Scopus subject areas

  • Analysis


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