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Large deviations for a class of tempered subordinators and their inverse processes
Proceedings of the Royal Society of Edinburgh Section A: Mathematics ( IF 1.3 ) Pub Date : 2021-01-08 , DOI: 10.1017/prm.2020.95
Nikolai Leonenko , Claudio Macci , Barbara Pacchiarotti

We consider a class of tempered subordinators, namely a class of subordinators with one-dimensional marginal tempered distributions which belong to a family studied in [3]. The main contribution in this paper is a non-central moderate deviations result. More precisely we mean a class of large deviation principles that fill the gap between the (trivial) weak convergence of some non-Gaussian identically distributed random variables to their common law, and the convergence of some other related random variables to a constant. Some other minor results concern large deviations for the inverse of the tempered subordinators considered in this paper; actually, in some results, these inverse processes appear as random time-changes of other independent processes.

中文翻译:

一类调和从属及其逆过程的大偏差

我们考虑一类回火下属,即一类具有一维边缘回火分布的下属,属于[3]中研究的一个家族。本文的主要贡献是非中心中等偏差结果。更准确地说,我们指的是一类大偏差原则,它填补了一些非高斯同分布随机变量的(平凡的)弱收敛到它们的普通定律,以及一些其他相关的随机变量收敛到一个常数之间的空白。其他一些次要结果涉及本文考虑的回火从属子的倒数的大偏差;实际上,在某些结果中,这些逆过程表现为其他独立过程的随机时间变化。
更新日期:2021-01-08
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