Bounds for the expected supremum of some non-stationary Gaussian processes

被引：0

作者：

Jafari, Hossein ^{[1
]}

Zhao, Yiqiang Q. ^{[2
]}

机构：

[1] Chabahar Maritime Univ, Dept Math, Chabahar, Iran

[2] Carleton Univ, Sch Math & Stat, Ottawa, ON, Canada

来源：

STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES | 2022年 / 94卷 / 07期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Non-stationary Gaussian process; Malliavin calculus; subfractional Brownian motion; bifractional Brownian motion; multifractional Brownian motion; FRACTIONAL BROWNIAN-MOTION; RUIN PROBABILITY; CALL CENTER; EXTREMES;

D O I：

10.1080/17442508.2021.2018445

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this article is to obtain closed-form lower and upper bounds for the expectation of the supremum of some non-stationary Gaussian processes. This supremum is an important quantity in applications such as finance and queueing systems. The covariance function structure, decomposition of the processes and probability inequalities are applied for some examples of non-stationary Gaussian processes, including sub-fractional, bifractional and multifractional Brownian motions. Malliavin calculus operators are also applied in some cases to find bounds for the density and expectation of the supremum of these processes.

引用

页码：1031 / 1053

页数：23

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