算子分数布朗运动的连续性模量

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Theoretical Probability Pub Date : 2023-12-15 DOI:10.1007/s10959-023-01307-z

Wensheng Wang

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引用次数: 0

摘要

研究了指数为 D 的算子分数布朗运动（包括多元分数布朗运动）的几乎确定的样本路径行为。特别是建立了样本路径的全局和局部连续性模量。这些结果表明，样本路径的全局和局部连续性模量完全由指数 D 的特征值实部以及某个单位向量的协方差矩阵决定。这些结果适用于多元分数布朗运动。

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The Moduli of Continuity for Operator Fractional Brownian Motion

The almost-sure sample path behavior of the operator fractional Brownian motion with exponent D, including multivariate fractional Brownian motion, is investigated. In particular, the global and the local moduli of continuity of the sample paths are established. These results show that the global and the local moduli of continuity of the sample paths are completely determined by the real parts of the eigenvalues of the exponent D, as well as the covariance matrix at some unit vector. These results are applicable to multivariate fractional Brownian motion.

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来源期刊

Journal of Theoretical Probability 数学-统计学与概率论

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： Journal of Theoretical Probability publishes high-quality, original papers in all areas of probability theory, including probability on semigroups, groups, vector spaces, other abstract structures, and random matrices. This multidisciplinary quarterly provides mathematicians and researchers in physics, engineering, statistics, financial mathematics, and computer science with a peer-reviewed forum for the exchange of vital ideas in the field of theoretical probability.