Intersection local time for two independent fractional Brownian motions

2007/04/10 by David Nualart, Nualart, David, Salvador Ortiz-Latorre +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #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.0704.1259

openalex publication_date 2007/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the existence of the intersection local time for two independent, d -dimensional fractional Brownian motions with the same Hurst parameter H. Assume d greater or equal to 2, then the intersection local time exists if and only if Hd<2.

Citations

• 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

Related

• Regularity of Intersection Local Times of Fractional Brownian Motions
• Higher-order derivative of intersection local time for two independent fractional Brownian motions
• Functional limit theorem for the self-intersection local time of the\n fractional Brownian motion
• Derivative for the intersection local time of fractional Brownian Motions
• 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