论文标题
关于在非凡的分支稳定过程中添加剂的终端价值定律
On the law of terminal value of additive martingales in a remarkable branching stable process
论文作者
论文摘要
我们在一个非凡的分支稳定过程中对末端价值$ W $的终端价值定律进行了明确描述。我们表明，端子值的右尾概率呈指数速度衰减，左尾概率概率得出，$ - \ log \ mathbb {p}（w <x）\ sim \ sim \ sim \ frac {1} {2} {2} {\ log x）^2 $ as $ x \ rightArrow 0+$。这些与文献中的结果形成鲜明对比，例如Liu（2000，2001）和Buraczewski（2009）。我们进一步表明，$ w $的法律是可以自我解释的，因此具有单峰密度。我们以$ 0 $和后者的$+\ infty $指定渐近行为。
We give an explicit description of the law of terminal value $W$ of additive martingales in a remarkable branching stable process. We show that the right tail probability of the terminal value decays exponentially fast and the left tail probability follows that $-\log \mathbb{P}(W<x) \sim \frac{1}{2} (\log x)^2$ as $x \rightarrow 0+$. These are in sharp contrast with results in the literature such as Liu (2000, 2001) and Buraczewski (2009). We further show that the law of $W$ is self-decomposable, and therefore, possesses a unimodal density. We specify the asymptotic behavior at $0$ and at $+\infty$ of the latter.
