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Harris","submitted_at":"2015-06-03T23:12:29Z","abstract_excerpt":"We study a dyadic branching Brownian motion on the real line with absorption at 0, drift $\\mu \\in \\mathbb{R}$ and started from a single particle at position $x>0.$ When $\\mu$ is large enough so that the process has a positive probability of survival, we consider $K(t),$ the number of individuals absorbed at 0 by time $t$ and for $s\\ge 0$ the functions $\\omega_s(x):= \\mathbb{E}^x[s^{K(\\infty)}].$ We show that $\\omega_s<\\infty$ if and only of $s\\in[0,s_0]$ for some $s_0>1$ and we study the properties of these functions. 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Harris","submitted_at":"2015-06-03T23:12:29Z","abstract_excerpt":"We study a dyadic branching Brownian motion on the real line with absorption at 0, drift $\\mu \\in \\mathbb{R}$ and started from a single particle at position $x>0.$ When $\\mu$ is large enough so that the process has a positive probability of survival, we consider $K(t),$ the number of individuals absorbed at 0 by time $t$ and for $s\\ge 0$ the functions $\\omega_s(x):= \\mathbb{E}^x[s^{K(\\infty)}].$ We show that $\\omega_s<\\infty$ if and only of $s\\in[0,s_0]$ for some $s_0>1$ and we study the properties of these functions. 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