Limiting distribution of the rightmost particle in catalytic branching Brownian motion

Sergey Bocharov, Simon C. Harris

Research output: Contribution to journalArticle

5 Citations (Scopus)
126 Downloads (Pure)

Abstract

We study the model of binary branching Brownian motion with spatially-inhomogeneous branching rate βδ0(·), where δ0(·) is the Dirac delta function and β is some positive constant. We show that the distribution of the rightmost particle centred about β/2 t converges to a mixture of Gumbel distributions according to a martingale limit. Our results form a natural extension to S. Lalley and T. Sellke [10] for the degenerate case of catalytic branching.

Original languageEnglish
Article numberPaper no. 70
Number of pages12
JournalElectronic Communications in Probability
Volume21
DOIs
Publication statusPublished - 4 Oct 2016

Keywords

  • Brownian motion
  • Catalytic branching
  • Local time

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