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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	199-219
Number of pages	21
Journal	Journal of Functional Analysis
Volume	249
Issue number	1
DOIs	https://doi.org/10.1016/j.jfa.2007.04.017
Publication status	Published - 1 Aug 2007
Externally published	Yes

Keywords

Fractional Brownian motion
Local time
N-Parameter d-dimensional Brownian motion
Quasi-sure existence
Self-intersection local time
Smooth semimartingale

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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 - Ren, Jiagang

AU - Zhang, Xicheng

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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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DO - 10.1016/j.jfa.2007.04.017

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VL - 249

SP - 199

EP - 219

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 1

ER -

Regularity of local times of random fields

Abstract

Keywords

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