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An integral test on time dependent local extinction for super-coalescing Brownian motion with Lebesgue initial measure
- Publication Year :
- 2009
-
Abstract
- This paper concerns the almost sure time dependent local extinction behavior for super-coalescing Brownian motion $X$ with $(1+\beta)$-stable branching and Lebesgue initial measure on $\bR$. We first give a representation of $X$ using excursions of a continuous state branching process and Arratia's coalescing Brownian flow. For any nonnegative, nondecreasing and right continuous function $g$, put \tau:=\sup \{t\geq 0: X_t([-g(t),g(t)])>0 \}. We prove that $\bP\{\tau=\infty\}=0$ or 1 according as the integral $\int_1^\infty g(t)t^{-1-1/\beta} dt$ is finite or infinite.<br />Comment: 14 pages
- Subjects :
- Mathematics - Probability
60G57, 60J80
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.0911.0774
- Document Type :
- Working Paper