Derivative of self-intersection local time for the sub-bifractional Brownian motion

Nenghui Kuang; Huantian Xie; Nenghui Kuang; Huantian Xie

doi:10.3934/math.2022573

AIMS Mathematics

2022, Volume 7, Issue 6: 10286-10302. doi: 10.3934/math.2022573

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Research article

Derivative of self-intersection local time for the sub-bifractional Brownian motion

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

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

Received: 26 December 2021 Revised: 22 February 2022 Accepted: 02 March 2022 Published: 24 March 2022
MSC : 60G22, 60J55

Let $ S^{H, K} = \{S^{H, K}_t, t\geq 0\} $ be the sub-bifractional Brownian motion (sbfBm) of dimension 1, with indices $ H\in (0, 1) $ and $ K\in (0, 1]. $ We mainly consider the existence of the self-intersection local time and its derivative for the sbfBm. Moreover, we prove its derivative is H$ \ddot{o} $lder continuous in space variable and time variable, respectively.
- sub-bifractional Brownian motion,
- self-intersection local time,
- derivative of self-intersection local time
Citation: Nenghui Kuang, Huantian Xie. Derivative of self-intersection local time for the sub-bifractional Brownian motion[J]. AIMS Mathematics, 2022, 7(6): 10286-10302. doi: 10.3934/math.2022573

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Abstract

Let $ S^{H, K} = \{S^{H, K}_t, t\geq 0\} $ be the sub-bifractional Brownian motion (sbfBm) of dimension 1, with indices $ H\in (0, 1) $ and $ K\in (0, 1]. $ We mainly consider the existence of the self-intersection local time and its derivative for the sbfBm. Moreover, we prove its derivative is H$ \ddot{o} $lder continuous in space variable and time variable, respectively.

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