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Existence, renormalization, and regularity properties of higher order derivatives of self-intersection local time of fractional Brownian motion
Stochastic Analysis and Applications ( IF 1.3 ) Pub Date : 2021-03-05 , DOI: 10.1080/07362994.2021.1893189 Kaustav Das 1 , Greg Markowsky 1
中文翻译:
分数布朗运动自交局部时间的高阶导数的存在性、重整化和规律性
更新日期:2021-03-05
Stochastic Analysis and Applications ( IF 1.3 ) Pub Date : 2021-03-05 , DOI: 10.1080/07362994.2021.1893189 Kaustav Das 1 , Greg Markowsky 1
Affiliation
Abstract
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.
中文翻译:
分数布朗运动自交局部时间的高阶导数的存在性、重整化和规律性
摘要
在 Yu 最近的一篇论文 (arXiv:2008.05633, 2020) 中,定义了分数布朗运动的自交局部时间的高阶导数,并证明了 Hurst 参数H在某些区域上的存在。利用维纳混沌展开,我们为 Yu 的结果提供了新的证明,并展示了如何使用 Varadhan 型重整化来扩展偶数导数的收敛范围。