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

2017/06/21 by Jingjun Guo, Guo, Jingjun, Yaozhong Hu +2 · 1 citation
Economics, Econometrics and Finance · Mathematics · #60G22 #60J55 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1706.06980

openalex publication_date 2017/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we obtain sharp conditions for the existence of the high order derivatives (k-th order) of intersection local time \widehatα(k)(0) of two independent d-dimensional fractional Brownian motions BH1t and \widetildeBH2s with Hurst parameters H1 and H2, respectively. We also study their exponential integrability.

Citations

• Derivative for the intersection local time of fractional Brownian Motions
• Renormalized self-intersection local time for fractional Brownian motion

Cited by

• On the exponential integrability of the derivative of intersection and self-intersection local time for fractional Brownian motion and a limit theorem related to the self-intersection local time for fractional Brownian motion

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