HIDA DISTRIBUTION CONSTRUCTION OF NON-GAUSSIAN REFLECTION POSITIVE GENERALIZED RANDOM FIELDS-Reference-Cited by-同舟云学术

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

Published:2009-03 Issue:01 Volume:12 Page:21-49
ISSN:0219-0257
Container-title:Infinite Dimensional Analysis, Quantum Probability and Related Topics
language:en
Short-container-title:Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

Author:

ALBEVERIO SERGIO¹,YOSHIDA MINORU W.²

Affiliation:

1. Inst. Angewandte Mathematik, Universität Bonn, Wegelerstr. 6, D-53115 Bonn, Germany

2. Dept. Math., Kansai Univ., Yamate-Chyou 3-3-35 Suita, Osaka 561-8680, Japan

Abstract

Multiple stochastic integrals with respect to the Gaussian white noise indexed by Rd are used for the construction of reflection positive non-Gaussian [Formula: see text] 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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Mathematical Physics,Statistics and Probability,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219025709003550

Reference54 articles.

1. On the Essential Self-Adjointness of Wick Powers of Relativistic Fields and of Fields Unitary Equivalent to Random Fields

2. CONVOLUTED GENERALIZED WHITE NOISE, SCHWINGER FUNCTIONS AND THEIR ANALYTIC CONTINUATION TO WIGHTMAN FUNCTIONS

3. Uniqueness and the global Markov property for Euclidean fields. The case of trigonometric interactions

4. Classical Dirichlet forms on topological vector spaces—Closability and a Cameron-Martin formula

5. H−C1 Maps and elliptic SPDEs with polynomial and exponential perturbations of Nelson's Euclidean free field

Cited by 4 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. A PDE Construction of the Euclidean $$\Phi ^4_3$$ Quantum Field Theory;Communications in Mathematical Physics;2021-04-15

2. Generalized Gramians: Creating frame vectors in maximal subspaces;Analysis and Applications;2016-11-18

3. A homeomorphism relating path spaces of stochastic processes with values in ℝℤ respectively (S1)ℤ;Infinite Dimensional Analysis, Quantum Probability and Related Topics;2014-03

4. A universal envelope for Gaussian processes and their kernels;Journal of Applied Mathematics and Computing;2013-04-20