On the exponential integrability of the derivative of intersection and self-intersection local time for Brownian motion and related processes

被引：0
|
作者：
Das, Kaustav [1 ,2 ]
Markowsky, Gregory [1 ]
Wu, Binghao [1 ]
机构：
[1] Monash Univ, Sch Math, Melbourne, Vic 3800, Australia
[2] Monash Univ, Ctr Quantitat Finance & Investment Strategies, Melbourne, Vic 3800, Australia
来源：
STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2025年 / 183卷
基金：
澳大利亚研究理事会;
关键词：
Brownian motion; Local time; Self-intersection local time; Derivatives of self-intersection local time; Fractional Brownian motion; Exponential integrability; DEVIATIONS;
D O I：
10.1016/j.spa.2025.104592
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We show that the derivative of the intersection and self-intersection local times of alpha-stable processes are exponentially integrable for certain parameter values. This includes the Brownian motion case. We also discuss related results present in the literature for fractional Brownian motion, and in particular give a counter-example to a result in Guo et al. (2019) related to this question.
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页数：14
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