Smoothness of local times of semimartingales

Hélène Airault; Ren Jiagang; Xicheng Zhang

doi:10.1016/S0764-4442(00)00251-2

Smoothness of local times of semimartingales

Hélène Airault^*, Ren Jiagang, Xicheng Zhang

^*Corresponding author for this work

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

18 Citations (Scopus)

Abstract

In this paper, applying the K-method in the real interpolation theory we show that for some semimartingales, their local times considered as functionals on the Wiener space belong to the fractional Sobolev spaces on the Wiener space Dpα for p > 1 and α < 1/2. Moreover, for the Brownian motion, we can prove that the result for the regularity of the local time as a functional on the Wiener space is optimal.

Original language	English
Pages (from-to)	719-724
Number of pages	6
Journal	Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume	330
Issue number	8
DOIs	https://doi.org/10.1016/S0764-4442(00)00251-2
Publication status	Published - 15 Apr 2000
Externally published	Yes

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10.1016/S0764-4442(00)00251-2

Cite this

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abstract = "In this paper, applying the K-method in the real interpolation theory we show that for some semimartingales, their local times considered as functionals on the Wiener space belong to the fractional Sobolev spaces on the Wiener space Dpα for p > 1 and α < 1/2. Moreover, for the Brownian motion, we can prove that the result for the regularity of the local time as a functional on the Wiener space is optimal.",

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AU - Airault, Hélène

AU - Jiagang, Ren

AU - Zhang, Xicheng

PY - 2000/4/15

Y1 - 2000/4/15

N2 - In this paper, applying the K-method in the real interpolation theory we show that for some semimartingales, their local times considered as functionals on the Wiener space belong to the fractional Sobolev spaces on the Wiener space Dpα for p > 1 and α < 1/2. Moreover, for the Brownian motion, we can prove that the result for the regularity of the local time as a functional on the Wiener space is optimal.

AB - In this paper, applying the K-method in the real interpolation theory we show that for some semimartingales, their local times considered as functionals on the Wiener space belong to the fractional Sobolev spaces on the Wiener space Dpα for p > 1 and α < 1/2. Moreover, for the Brownian motion, we can prove that the result for the regularity of the local time as a functional on the Wiener space is optimal.

UR - https://www.scopus.com/pages/publications/0038600495

U2 - 10.1016/S0764-4442(00)00251-2

DO - 10.1016/S0764-4442(00)00251-2

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SN - 0764-4442

VL - 330

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JO - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

JF - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

IS - 8

ER -

Smoothness of local times of semimartingales

Abstract

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