关于Bacry和Muzy极限对数不可分随机测度的矩的注记
A Note on Moments of Limit Log Infinitely Divisible Stochastic Measures of Bacry and Muzy
摘要：
推导了Bacry和Muzy [ $\textit{Comm. Math. Phys.}$ ${\bf 236}$：449-475，2003]的极限对数无限可分随机测度的总质量的单个和联合矩的多重积分表示.测量的总质量的协方差结构显示为对数。提出了极限测度单阶矩所对应的Selberg积分的一个推广，并证明了它满足一个递推关系。将极限对数正态测度、经典Selberg积分与$λ_1=λ_2=0,$及Morris积分的联合矩表示为多重二项式和的形式.为了应用，精确计算了极限对数泊松测度的低阶矩，并详细讨论了极限对数正态测度的低阶联合矩。
英文摘要：
A multiple integral representation of single and joint moments of the total mass of the limit log-infinitely divisible stochastic measure of Bacry and Muzy [$\textit{Comm. Math. Phys.}$ ${\bf 236}$: 449-475, 2003] is derived. The covariance structure of the total mass of the measure is shown to be logarithmic. A generalization of the Selberg integral corresponding to single moments of the limit measure is proposed and shown to satisfy a recurrence relation. The joint moments of the limit lognormal measure, classical Selberg integral with $λ_1=λ_2=0,$ and Morris integral are represented in the form of multiple binomial sums. For application, low moments of the limit log-Poisson measure are computed exactly and low joint moments of the limit lognormal measure are considered in detail.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
