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.

引用

页码：133 / 157

页数：25

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