Existence, renormalization, and regularity properties of higher order derivatives of self-intersection local time of fractional Brownian motion

被引：5
|
作者：
Das, Kaustav [1 ]
Markowsky, Greg [1 ]
机构：
[1] Monash Univ, Sch Math, Clayton, Vic 3800, Australia
来源：
STOCHASTIC ANALYSIS AND APPLICATIONS | 2022年 / 40卷 / 01期
关键词：
Self-intersection local time; derivatives of self-intersection local time; fractional Brownian motion; Wiener chaos;
D O I：
10.1080/07362994.2021.1893189
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In a recent paper by Yu (arXiv:2008.05633, 2020), higher order derivatives of self-intersection local time of fractional Brownian motion were defined, and existence over certain regions of the Hurst parameter H was proved. Utilizing the Wiener chaos expansion, we provide new proofs of Yu's results and show how a Varadhan-type renormalization can be used to extend the range of convergence for the even derivatives.
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页码：133 / 157
页数：25
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