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

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.

Keywords

• sub-bifractional brownian motion
• self-intersection local time
• derivative of self-intersection local time