论文标题
布尔添加卷积的差异函数
Variance function of boolean additive convolution
论文作者
论文摘要
假设Vν是cauchy-stieltjes内核（CSK）家族K+（ν）的伪变量函数，该家族是由非退化概率度量ν产生的，并从上方界限。我们在布尔添加卷积功率下确定伪变化函数（或方差函数Vν）的公式。该公式用于确定概率度量之间的布尔贝尔科维奇 - 巴特（Bercovici-bata）培养下方差函数之间的关系。我们还提供了布尔累积物与方差函数之间的联系，我们将某些概率度量的布尔累积物与加泰罗尼亚的数字和加泰罗尼亚的数字联系起来。
Suppose Vν is the pseudo-variance function of the Cauchy-Stieltjes Kernel (CSK) family K+(ν) generated by a non degenerate probability measure ν with support bounded from above. We determine the formula for pseudo-variance function (or variance function Vν in case of existence) under boolean additive convolution power. This formulas is used to identify the relation between variance functions under Boolean Bercovici-Bata Bijection between probability measures. We also gives the connection between boolean cumulants and variance function and we relate boolean cumulants of some probability measures to Catalan numbers and Fuss Catalan numbers.
