Higher-order derivative of intersection local time for two independent fractional Brownian motions

Abstract

In this article, we obtain sharp conditions for the existence of the high order derivatives ($k$-th order) of intersection local time ${\hat{\alpha }}^{(k)}(0)$ of two independent d-dimensional fractional Brownian motions $B_t^{H_1}$ and ${\tilde{B}}_s^{H_2}$ with Hurst parameters $H_1$ and $H_2$, respectively. We also study their exponential integrability.

arXiv comment10 pages

References in corpus (3)

• Renormalized self-intersection local time for fractional Brownian motion
• Intersection local times of independent fractional Brownian motions as generalized white noise functionals
• Derivative for the intersection local time of fractional Brownian Motions

Cited by in corpus (2)

• Strong Uniqueness of Singular Stochastic Delay Equations
• Limit theorems for functionals of two independent Gaussian processes