论文标题
指数密度和复合泊松措施
Exponential densities and compound Poisson measures
论文作者
论文摘要
我们证明了卷积无穷大的估算值$ f^{n \ star} $，以及相应的复合泊松泊松测量的密度，用于一类径向降低的降低密度，$ \ mathbb {r}^d $，$ d \ geq 1 $，这不是相当于的。现有的方法和工具仅限于卷积$ f^{2 \ star}（x）$与Infinity的初始密度$ f（x）$相当的情况。我们提出了一种新方法，该方法可以打破这个障碍。我们专注于密度是指数函数和较小订单项的产品 - 它们在应用中很常见。在较小的订单项为多项式估计的情况下，根据广义贝塞尔函数给出。我们的结果可以看作是理解复合泊松的复杂渐近特性以及针对此类密度构建的更一般的无限分区措施的首次尝试。
We prove estimates at infinity of convolutions $f^{n\star}$ and densities of the corresponding compound Poisson measures for a class of radial decreasing densities on $\mathbb{R}^d$, $d \geq 1$, which are not convolution equivalent. Existing methods and tools are limited to the situation in which the convolution $f^{2\star}(x)$ is comparable to initial density $f(x)$ at infinity. We propose a new approach which allows one to break this barrier. We focus on densities which are products of exponential functions and smaller order terms -- they are common in applications. In the case when the smaller order term is polynomial estimates are given in terms of the generalized Bessel function. Our results can be seen as the first attempt to understand the intricate asymptotic properties of the compound Poisson and more general infinitely divisible measures constructed for such densities.
