多混合分数布朗运动与Ornstein-Uhlenbeck过程

IF 0.7 Q3 STATISTICS & PROBABILITY

Modern Stochastics-Theory and Applications Pub Date : 2023-01-01 DOI:10.15559/23-vmsta229

Hamidreza Maleki Almani, T. Sottinen

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引用次数: 0

摘要

研究了多混合分数布朗运动(mmfBm)和多混合分数Ornstein-Uhlenbeck过程(mmfOU)。这些过程分别是通过叠加或混合(无限多个)独立的分数阶布朗运动(fBm)和分数阶Ornstein-Uhlenbeck过程(fOU)来混合构建的。证明了它们作为${L^{2}}$过程的存在性，并研究了它们的路径性质，即长程和短程依赖、Hölder连续性、p变分和条件完全支持。

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Multi-mixed fractional Brownian motions and Ornstein–Uhlenbeck processes

The so-called multi-mixed fractional Brownian motions (mmfBm) and multi-mixed fractional Ornstein–Uhlenbeck (mmfOU) processes are studied. These processes are constructed by mixing by superimposing or mixing (infinitely many) independent fractional Brownian motions (fBm) and fractional Ornstein–Uhlenbeck processes (fOU), respectively. Their existence as ${L^{2}}$ processes is proved, and their path properties, viz. long-range and short-range dependence, Hölder continuity, p-variation, and conditional full support, are studied.

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来源期刊

Modern Stochastics-Theory and Applications STATISTICS & PROBABILITY-

CiteScore

1.30

自引率

50.00%

发文量

审稿时长

10 weeks