HIDA DISTRIBUTION CONSTRUCTION OF NON-GAUSSIAN REFLECTION POSITIVE GENERALIZED RANDOM FIELDS

被引：3

作者：

Albeverio, Sergio ^{[1
]}

Yoshida, Minoru W. ^{[2
]}

机构：

[1] Univ Bonn, Inst Angew Math, D-53115 Bonn, Germany

[2] Kansai Univ, Dept Math, Osaka 5618680, Japan

来源：

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS | 2009年 / 12卷 / 01期

关键词：

Hida distribution; multiple stochastic integral; Wick powers; relativistic fields; Euclidean fields; S-transform; WICK POWER-SERIES; RELATIVISTIC FIELDS; SAMPLE PATHS; WHITE-NOISE; MARKOV; CONTINUITY; AXIOMS;

D O I：

10.1142/S0219025709003550

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Multiple stochastic integrals with respect to the Gaussian white noise indexed by R-d are used for the construction of reflection positive non-Gaussian S'(Rd) valued random variables (random fields). This construction is then extended to a class of Hida distribution to consider several interesting examples. In particular, some new fields (without full Euclidean invariance but satisfying all other axioms, including space rotation invariance) are constructed through this probabilistic (and purely Euclidean) procedure.

引用

页码：21 / 49

页数：29

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