The frontier of a branching Brownian motion with killing
Abstract
We consider a branching Brownian motion with killing which starts with a single particle at the origin, for which the instantaneous branching and killing rates of a particle at position x are $\beta(x)$ and k(x) respectively. We show that if $\beta$ is continuous and bounded and $k(x)\uparrow\infty$ as $\vert x\vert\to\infty$ then $R\sb{t},$ the right frontier at time t, grows sublinearly as $t\to\infty.$ For the class of killing functions $k\sb\alpha(x)=\vert x\vert\sp\alpha,$ $\alpha > 0$ we show that $R\sb{t}\ {a.s.\atop\sim}\ c\sb\alpha t\sp{2/\alpha +2}$ as $t\to\infty,$ for some constant $c\sb\alpha > 0.$
Degree
Ph.D.
Advisors
Lalley, Purdue University.
Subject Area
Statistics|Mathematics
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