Higher order derivative of self-intersection local time for fractional Brownian motion

2020/08/13 by Qian Yu, Yu, Qian · 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.2008.05633

openalex publication_date 2020/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the existence and Hölder continuity conditions for the k-th order derivatives of self-intersection local time for d-dimensional fractional Brownian motion, where k=(k₁,k₂,⋯, k_d). Moreover, we show a limit theorem for the critical case with H=(2)/(3) and d=1, which was conjectured by Jung and Markowsky (2014).

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

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