分数布朗运动多重局部时的存在性与光滑性

doi:10.6040/j.issn.1671-9352.0.2024.345

摘要/Abstract

摘要： 给出一维分数布朗运动多重局部时的Wiener混沌分解,证明其存在性和光滑性,将相关结果推广至d-维分数布朗运动(d≥2),给出当x=0时,d-维分数布朗运动多重局部时的Wiener混沌分解和光滑性。

Abstract: The Wiener chaos decomposition for the multiple local time of one-dimensional fractional Brownian motion is established. Its existence and smoothness are proved. The relevant results are extended to the d-dimensional fractional Brownian motion for d≥2. When x=0, the Wiener chaos decomposition and smoothness for the multiple local time of d-dimensional fractional Brownian motion are obtained.

Key words: fractional Brownian motion, local time, Wiener chaos decomposition, smoothness

中图分类号:

O211

张翠芸,郭精军,胡峰. 分数布朗运动多重局部时的存在性与光滑性[J]. 《山东大学学报(理学版)》, 2026, 61(9): 64-73.

ZHANG Cuiyun, GUO Jingjun, HU Feng. Existence and smoothness for multiple local time of fractional Brownian motion[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2026, 61(9): 64-73.

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