ISSN:
1432-2064
Keywords:
Mathematics Subject Classification (1991): Primary 60J80; Secondary 60J55, 60G57
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary. A super-Brownian motion $X$ in ${\Bbb R}$ with “hyperbolic” branching rate $\varrho _2(b)=1/b^2$ , $\;b\in {\Bbb R},\,$ is constructed, which symbolically could be described by the formal stochastic equation \begin{equation} {\rm d}X_t\,=\,\textstyle \frac 12\,\Delta X_t\,{\rm d}t+\sqrt{2\varrho _2X_t% }\,{\rm d}W_{t\,},\qquad t〉0, \label{stochequ} \end{equation} (with a space-time white noise ${\rm d}W$ ). Starting at $X_0=\delta _{a\,},$ $\,a\ne 0,$ this superprocess $X$ will never hit the catalytic center: There is an increasing sequence of Brownian stopping times $\tau _n$ strictly smaller than the hitting time of $\,0$ such that with probability one Dynkin's stopped measures $X_{\tau _n}$ vanish except for finitely many $n.$
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s004400050088
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