Multi-mixed fractional Brownian motions and Ornstein–Uhlenbeck processes
Multi-mixed fractional Brownian motions and Ornstein–Uhlenbeck processes
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多重混合分数布朗运动和 Ornstein-Uhlenbeck 过程
DOI：
10.15559/23-vmsta229
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发表时间：
2023
期刊：
影响因子：
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通讯作者：
T. Sottinen
中科院分区：
文献类型：
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作者：
Hamidreza Maleki Almani;T. Sottinen
研究了多重混合分数布朗运动（mmfBm）和多重混合分数Ornstein-Uhlenbeck（mmfBm）过程.这些过程分别通过叠加或混合（无穷多个）独立的分数布朗运动（fBM）和分数Ornstein-Uhlenbeck过程（fBM）来混合。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，即长程相关性、短程相关性、Hölder连续性、p-变差和条件全支撑性.
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.