Meixner classes and the square of white noise
Meixner classes and the square of white noise
复制标题
梅克斯纳类和白噪声平方
DOI：
10.1090/conm/317/05516
复制
发表时间：
2003
期刊：
影响因子：
--
通讯作者：
L. Accardi
中科院分区：
文献类型：
--
作者：
L. Accardi
一种新的（乘法）重整化方法的引入
导致了白色噪音平方的李代数，结果是
是李代数sl（2，\R）上的流代数。所有的
这个代数的表示具有某种不可约性
房地产正在建设中。一类单参数经典过程
是由发电机定义的。这些真空分布
过程被识别为三个例外（即非高斯
或Poisson）类。
这类
最近几位作者研究了分布，
在决策理论中出现的不同问题，数学
金融，量子场论，经典概率，$\dots$。在
本文最后一节将简要回顾这些发展。
The introduction of a new (multiplicative) renormalization procedure
leads to a Lie algebra for the square of white noise which turns out
to be a current algebra on the Lie algebra $sl(2, \R)$. All the
representations of this algebra enjoying a certain irreducibility
property are constructed. A one parameter class of classical processes
is defined in terms of the generators. The vacuum distributions of these
processes are identified with the three exceptional (i.e. non Gaussian
or Poisson) classes in the Meixner classification.
This class of
distributions has been recently studied by several authors in connection
with different problems arising in decision theory, mathematical
finance, quantum field theory, classical probability, $\dots$. In the
last section of the paper these developments will be quickly reviewed.