Open AccessDerivative of self-intersection local time for the sub-bifractional Brownian motion
Author(s) -
Nenghui Kuang,
Huiqing 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.