Sharp bounds on the density, Green function and jumping function of subordinate killed BM

Research output: Contribution to journalArticle

Abstract

Subordination of a killed Brownian motion in a domain D ⊂ ℝd via an α/2-stable subordinator gives rise to a process Zt whose infinitesimal generator is -(-Δ|D) α/2, the fractional power of the negative Dirichlet Laplacian. In this paper we establish upper and lower estimates for the density, Green function and jumping function of Zt when D is either a bounded C 1,1 domain or an exterior C1,1 domain. Our estimates are sharp in the sense that the upper and lower estimates differ only by a multiplicative constant.

Original languageEnglish (US)
Pages (from-to)606-628
Number of pages23
JournalProbability Theory and Related Fields
Volume128
Issue number4
DOIs
StatePublished - Apr 1 2004

Keywords

  • Fractional Laplacian
  • Green function
  • Jumping function
  • Killed Brownian motions
  • Stable processes
  • Subordination
  • Transition density

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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