Multiparameter multifractional Brownian motion: Local nondeterminism and joint continuity of the local times

被引：16

作者：

Ayache, Antoine ^{[1
]}

Shieh, Narn-Rueih ^{[2
]}

Xiao, Yimin ^{[3
]}

机构：

[1] Univ Lille 1, UMR CNRS 8524, Lab Paul Painleve, F-59655 Villeneuve Dascq, France

[2] Natl Taiwan Univ, Dept Math, Taipei 10617, Taiwan

[3] Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48824 USA

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2011年 / 47卷 / 04期

基金：

美国国家科学基金会;

关键词：

Multifractional Brownian motion; Local nondeterminism; Local times; Joint continuity; HOLDER CONDITIONS; PATH PROPERTIES; DIMENSION;

D O I：

10.1214/10-AIHP408

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

By using a wavelet method we prove that the harmonisable-type N-parameter multifractional Brownian motion (mfBm) is a locally nondeterministic Gaussian random field. This nice property then allows us to establish joint continuity of the local times of an (N, d)-mfBm and to obtain some new results concerning its sample path behavior.

引用

页码：1029 / 1054

页数：26

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