Reflection Negative Kernels and Fractional Brownian Motion

被引：0

作者：

Jorgensen, Palle E. T. ^{[1
]}

Neeb, Karl-Hermann ^{[2
]}

Olafsson, Gestur ^{[3
]}

机构：

[1] Univ Iowa, Dept Math, Iowa City, IA 52242 USA

[2] FAU Erlangen Nurnberg, Dept Math, Cauerstr 11, D-91058 Erlangen, Germany

[3] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA

来源：

SYMMETRY-BASEL | 2018年 / 10卷 / 06期

关键词：

fractional brownian motion; reflection positivity; reflection negative kernels; representations of SL2 (R); PATHWISE PROJECTIVE INVARIANCE; UNITARY REPRESENTATIONS; REPRODUCING KERNELS; GAUSSIAN-PROCESSES; HILBERT-SPACE; SYMMETRY;

D O I：

10.3390/sym10060191

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In this article we study the connection of fractional Brownian motion, representation theory and reflection positivity in quantum physics. We introduce and study reflection positivity for affine isometric actions of a Lie group on a Hilbert space epsilon and show in particular that fractional Brownian motion for Hurst index 0 < H <= 1/2 is reflection positive and leads via reflection positivity to an infinite dimensional Hilbert space if 0 < H < 1/2. We also study projective invariance of fractional Brownian motion and relate this to the complementary series representations of GL(2) (R). We relate this to a measure preserving action on a Gaussian L-2-Hilbert space L-2 (epsilon).

引用

页数：39

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