We construct and describe the extremal process for?variable speed branching Brownian motion, studied recently by Fang and Zeitouni, for the case of piecewise constant speeds; in fact for simplicity we concentrate on the case when the speed is $sigma_1$ for $sleq bt$ and $sigma_2$ when $btleq sleq t$. In the case $sigma_1>sigma_2$, the process is the concatenation of two BBM extremal processes, as expected. In the case $sigma_1展开▼
机译:对于分段恒定速度的情况,Fang和Zeitouni最近研究了变速分支布朗运动的极值过程,并对其进行了描述。实际上,为简单起见,我们专注于$ s leq bt $的速度为$ sigma_1 $和$ bt leq s leq t $的情况下$ sigma_2 $的情况。在$ sigma_1> sigma_2 $的情况下,该过程是两个BBM极值过程的串联,正如预期的那样。在$ sigma_1 < sigma_2 $的情况下,出现了一个新的群集点过程系列,它们与BBM过程相似但明显不同。我们的证明遵循Arguin,Bovier和Kistler的策略。
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