论文标题
复合泊松总和的次指数密度和随机步行的至上
Subexponential densities of compound Poisson sums and the supremum of a random walk
论文作者
论文摘要
我们用$ [0，\ infty）$的复合泊松分布的$（0，\ infty）$上的次指定密度表征了亚指数密度。作为推论，我们表明在$ \ Mathbb r _+$上，所有亚指数概率密度函数的类别都在复合泊松总和的广义卷积根下关闭。此外，我们将$（0，\ infty）$上的次指定密度申请，以分配随机步行的上限。
We characterize the subexponential densities on $(0,\infty)$ for compound Poisson distributions on $[0,\infty)$ with absolutely continuous Lévy measures. As a corollary, we show that the class of all subexponential probability density functions on $\mathbb R_+$ is closed under generalized convolution roots of compound Poisson sums. Moreover, we give an application to the subexponential density on $(0,\infty)$ for the distribution of the supremum of a random walk.
