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Functional central limit theorems for multivariate Bessel processes in the freezing regime
Stochastic Analysis and Applications ( IF 1.3 ) Pub Date : 2020-07-05 , DOI: 10.1080/07362994.2020.1786402
Michael Voit 1 , Jeannette H. C. Woerner 1
Affiliation  

Abstract Multivariate Bessel processes describe interacting particle systems of Calogero-Moser-Sutherland type and are related with β-Hermite and β-Laguerre ensembles. They depend on a root system and a multiplicity k. Recently, several limit theorems were derived for with fixed starting point. Moreover, the SDEs of were used to derive strong laws of large numbers for with starting points of the form with x in the interior of the Weyl chambers. Here we provide associated almost sure functional central limit theorems which are locally uniform in t. The Gaussian limit processes admit explicit representations in terms of the solutions of associated deterministic ODEs.

中文翻译:

冻结状态下多元贝塞尔过程的函数中心极限定理

摘要 多元贝塞尔过程描述了 Calogero-Moser-Sutherland 类型的相互作用粒子系统,并且与 β-Hermite 和 β-Laguerre 系综有关。它们取决于根系统和多样性 k。最近,一些极限定理被推导出固定起点。此外, 的 SDE 被用来推导出强大的大数定律,其中 x 形式的起点在外尔室的内部。在这里,我们提供了相关的几乎肯定的泛函中心极限定理,它们在 t 中是局部一致的。高斯极限过程允许根据相关确定性 ODE 的解进行显式表示。
更新日期:2020-07-05
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