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Large deviations for functionals of some self-similar Gaussian processes
Stochastics ( IF 0.8 ) Pub Date : 2020-01-30 , DOI: 10.1080/17442508.2020.1720018
Xiaoming Song 1
Affiliation  

ABSTRACT

We prove large deviation principles for 0tγ(Xs)ds, where X is a d-dimensional self-similar Gaussian process and γ(x) takes the form of the Dirac delta function δ(x), |x|β with β(0,d), or i=1d|xi|βi with βi(0,1). In particular, large deviations are obtained for the functionals of d-dimensional fractional Brownian motion, sub-fractional Brownian motion and bi-fractional Brownian motion. As an application, the critical exponential integrability of the functionals is discussed.



中文翻译:

一些自相似高斯过程的泛函有较大偏差

抽象的

我们证明了大偏差原理 0ŤγXsds,其中Xd维自相似高斯过程,γX 采用Dirac delta函数的形式 δX|X|-ββ0d, 或者 一世=1个d|X一世|-β一世β一世01个。特别地,对于d维分数布朗运动,子分数布朗运动和双分数布朗运动的函数获得大偏差。作为应用,讨论了功能的关键指数可集成性。

更新日期:2020-01-30
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