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

Nenghui Kuang | Zendy; Huantian Xie | Zendy

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

Author(s) -

Nenghui Kuang,

Huantian Xie

Publication year - 2022

Publication title -

aims mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.329

H-Index - 15

ISSN - 2473-6988

DOI - 10.3934/math.2022573

Subject(s) - intersection (aeronautics) , derivative (finance) , brownian motion , dimension (graph theory) , mathematics , local time , variable (mathematics) , motion (physics) , mathematical analysis , combinatorics , pure mathematics , physics , classical mechanics , statistics , financial economics , economics , engineering , aerospace engineering

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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