数学物理学报(英文版)

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INTERSECTIONS AND POLAR FUNCTIONS OF FRACTIONAL BROWNIAN SHEETS

陈振龙   

  1. 浙江工商大学统计与数学学院, 杭州 310018
  • 收稿日期:2006-08-20 修回日期:1900-01-01 出版日期:2008-10-20 发布日期:2008-10-20
  • 通讯作者: 陈振龙
  • 基金资助:

    Supported by the Key Research Base for Humanities and Social Sciences of Zhejiang Provincial High Education Talents (Statistics of Zhejiang Gongshang University), the Natural Science Foundation of Shaanxi Province (2005A08, 2006A14)

INTERSECTIONS AND POLAR FUNCTIONS OF FRACTIONAL BROWNIAN SHEETS

Chen Zhenlong   

  1. College of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China
  • Received:2006-08-20 Revised:1900-01-01 Online:2008-10-20 Published:2008-10-20
  • Contact: Chen Zhenlong

摘要:

Let BH={BH(t), t ∈ R+N} be a real-valued (N, d) fractional Brownian sheet with Hurst index H=(H1, …, HN). The characteristics of the polar functions for BH are discussed. The relationship between the class of continuous functions satisfying Lipschitz condition and the class of polar -functions of BH is obtained. The Hausdorff dimension about the fixed points and the inequality about the Kolmogorov’s entropy index for BH are presented. Furthermore, it is proved that any two independent fractional Brownian sheets are nonintersecting in some conditions. A problem proposed by LeGall about the existence of no-polar continuous functions satisfying the Hölder condition is also solved.

Abstract:

Let BH={BH(t), t ∈ R+N} be a real-valued (N, d) fractional Brownian sheet with Hurst index H=(H1, …, HN). The characteristics of the polar functions for BH are discussed. The relationship between the class of continuous functions satisfying Lipschitz condition and the class of polar-functions of BH is obtained. The Hausdorff dimension about the fixed points and the inequality about the Kolmogorov’s entropy index for BH are presented. Furthermore, it is proved that any two independent fractional Brownian sheets are nonintersecting in some conditions. A problem proposed by LeGall about the existence of no-polar continuous functions satisfying the Hölder condition is also solved.

Key words: Fractional Brownian sheet, polar function, Hausdorff dimension, intersection

中图分类号: 

  • 60G15