Regularity of local times of random fields

Jiagang Ren; Xicheng Zhang

doi:10.1016/j.jfa.2007.04.017

Regularity of local times of random fields

Jiagang Ren^*, Xicheng Zhang

^*此作品的通讯作者

科研成果: 期刊稿件 › 文章 › 同行评审

1 引用（Scopus）

摘要

In this paper, we study the fractional smoothness of local times of general processes starting from the occupation time formula, and obtain the quasi-sure existence of local times in the sense of the Malliavin calculus. This general result is then applied to the local times of N-parameter d-dimensional Brownian motions, fractional Brownian motions and the self-intersection local time of the 2-dimensional Brownian motion, as well as smooth semimartingales.

源语言	英语
页（从-至）	199-219
页数	21
期刊	Journal of Functional Analysis
卷	249
期	1
DOI	https://doi.org/10.1016/j.jfa.2007.04.017
出版状态	已出版 - 1 8月 2007
已对外发布	是

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Ren, J., & Zhang, X. (2007). Regularity of local times of random fields. Journal of Functional Analysis, 249(1), 199-219. https://doi.org/10.1016/j.jfa.2007.04.017

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abstract = "In this paper, we study the fractional smoothness of local times of general processes starting from the occupation time formula, and obtain the quasi-sure existence of local times in the sense of the Malliavin calculus. This general result is then applied to the local times of N-parameter d-dimensional Brownian motions, fractional Brownian motions and the self-intersection local time of the 2-dimensional Brownian motion, as well as smooth semimartingales.",

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AU - Zhang, Xicheng

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N2 - In this paper, we study the fractional smoothness of local times of general processes starting from the occupation time formula, and obtain the quasi-sure existence of local times in the sense of the Malliavin calculus. This general result is then applied to the local times of N-parameter d-dimensional Brownian motions, fractional Brownian motions and the self-intersection local time of the 2-dimensional Brownian motion, as well as smooth semimartingales.

AB - In this paper, we study the fractional smoothness of local times of general processes starting from the occupation time formula, and obtain the quasi-sure existence of local times in the sense of the Malliavin calculus. This general result is then applied to the local times of N-parameter d-dimensional Brownian motions, fractional Brownian motions and the self-intersection local time of the 2-dimensional Brownian motion, as well as smooth semimartingales.

KW - Fractional Brownian motion

KW - Local time

KW - N-Parameter d-dimensional Brownian motion

KW - Quasi-sure existence

KW - Self-intersection local time

KW - Smooth semimartingale

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VL - 249

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EP - 219

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 1

ER -

Regularity of local times of random fields

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