Long-range dependent completely correlated mixed fractional Brownian motion

被引：2

作者：

Dufitinema, Josephine ^{[1
]}

Shokrollahi, Foad ^{[2
]}

Sottinen, Tommi ^{[2
]}

Viitasaari, Lauri ^{[3
]}

机构：

[1] IQVIA, Global Database Studies, Real World Solut, Spektri Business Pk,Bldg Duo,Metsanneidonkuja 6, Espoo 02130, Finland

[2] Univ Vaasa, Sch Technol & Innovat, POB 700, Vaasa 65101, Finland

[3] Uppsala Univ, Dept Math, POB 480, S-75106 Uppsala, Sweden

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2024年 / 170卷

关键词：

Cameron-Martin-Girsanov-Hitsuda theorem; Fractional Brownian motion; Mixed fractional Brownian motion; Prediction; Transfer principle; STOCHASTIC CALCULUS; GAUSSIAN-PROCESSES; LAW;

D O I：

10.1016/j.spa.2023.104289

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper we introduce the long-range dependent completely correlated mixed fractional Brownian motion (ccmfBm). This is a process that is driven by a mixture of Brownian motion (Bm) and a long-range dependent completely correlated fractional Brownian motion (fBm, ccfBm) that is constructed from the Brownian motion via the Molchan-Golosov representation. Thus, there is a single Bm driving the mixed process. In the short time-scales the ccmfBm behaves like the Bm (it has Brownian Holder index and quadratic variation). However, in the long time-scales it behaves like the fBm (it has long-range dependence governed by the fBms Hurst index). We provide a transfer principle for the ccmfBm and use it to construct the Cameron-Martin-Girsanov-Hitsuda theorem and prediction formulas. Finally, we illustrate the ccmfBm by simulations.

引用

页数：15

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