Remark on It$ \hat{o} $ and Tanaka formulas of multidimensional bifractional Brownian motion

Nenghui Kuang; Huantian Xie; Nenghui Kuang; Huantian Xie

doi:10.3934/math.20261055

AIMS Mathematics

2026, Volume 11, Issue 8: 26301-26307. doi: 10.3934/math.20261055

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Research article

Remark on It$ \hat{o} $ and Tanaka formulas of multidimensional bifractional Brownian motion

Nenghui Kuang ^{1
,
,},
Huantian Xie ²

1.
School of Mathematics and Statistics, Hunan University of Science and Technology, Xiangtan, Hunan 411201, China
2.
School of Mathematics and Statistics, Linyi University, Linyi, Shandong 276005, China

Received: 17 April 2026 Revised: 23 July 2026 Accepted: 05 August 2026 Published: 24 August 2026
MSC : 60G12, 60G15, 60H05, 60H07

In this paper, by using the idea of Proposition 3.3 in Chen et al. (2024), we correct the proof of Lemma 2 in Es-sebaiy and Tudor (2007) about multidimensional bifractional Brownian motion: It$ \hat{o} $ and Tanaka formulas.
- bifractional Brownian motion,
- It$ \hat{o} $ formula,
- Tanaka formula,
- Cauchy-Schwarz inequality,
- fractional Brownian motion
Citation: Nenghui Kuang, Huantian Xie. Remark on It$ \hat{o} $ and Tanaka formulas of multidimensional bifractional Brownian motion[J]. AIMS Mathematics, 2026, 11(8): 26301-26307. doi: 10.3934/math.20261055

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Abstract

In this paper, by using the idea of Proposition 3.3 in Chen et al. (2024), we correct the proof of Lemma 2 in Es-sebaiy and Tudor (2007) about multidimensional bifractional Brownian motion: It$ \hat{o} $ and Tanaka formulas.

References

[1]	K. Es-sebaiy, C. A.Tudor, Multidimensional bifractional Brownian motion: It$\hat{o}$ and Tanaka formulas, Stoch. Dyn., 7 (2007), 365–388.
[2]	Y. Chen, Z. Ding, Y. Li, Berry-Ess$\acute{e}$en bounds and almost sure CLT for the quadratic variation of a class of Gaussian process, Commun. Stat. Theory Methods, 53 (2024), 3920–3939. https://doi.org/10.1080/03610926.2023.2167055 doi: 10.1080/03610926.2023.2167055

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