数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (5): 1860-1876.doi: 10.1016/S0252-9602(11)60366-4

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REMARKS ON SUB-FRACTIONAL BESSEL PROCESSES

申广君*|陈超|闫理坦   

  1. Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China;Department of Mathematics, Anhui Normal University, Wuhu 241000, China; Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China; Department of Mathematics, Donghua University, Shanghai 201620, China
  • 收稿日期:2010-03-03 出版日期:2011-09-20 发布日期:2011-09-20
  • 通讯作者: 申广君,guangjunshen@yahoo.com.cn E-mail:guangjunshen@yahoo.com.cn;mathscc@163.com;itanyan@dhu.edu.cn
  • 基金资助:

    Supported by the NSFC (10871041) and Key NSF of Anhui Educational Committe (KJ2011A139).

REMARKS ON SUB-FRACTIONAL BESSEL PROCESSES

 SHEN Guang-Jun*, CHEN Chao, YAN Li-Tan   

  1. Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China;Department of Mathematics, Anhui Normal University, Wuhu 241000, China; Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China; Department of Mathematics, Donghua University, Shanghai 201620, China
  • Received:2010-03-03 Online:2011-09-20 Published:2011-09-20
  • Contact: SHEN Guang-Jun,guangjunshen@yahoo.com.cn E-mail:guangjunshen@yahoo.com.cn;mathscc@163.com;itanyan@dhu.edu.cn
  • Supported by:

    Supported by the NSFC (10871041) and Key NSF of Anhui Educational Committe (KJ2011A139).

摘要:

Let S = {(S1t , ···, Sdt )}t≥0 denote a d-dimensional sub-fractional Brownianmotion with index H ≥ 1/2. In this paper we study some properties of the process X of the form
Xt :=∑di=1t0Sis/RsdSis, ≥ 1,
where Rt =√(S1t )2 + ··· + (Sdt )2 is the sub-fractional Bessel process.

关键词: sub-fractional Brownian motion, Malliavin calculus, sub-fractional Bessel processes, chaos expansion

Abstract:

Let S = {(S1t , ···, Sdt )}t≥0 denote a d-dimensional sub-fractional Brownianmotion with index H ≥ 1/2. In this paper we study some properties of the process X of the form
Xt :=∑di=1t0Sis/RsdSis, ≥ 1,
where Rt =√(S1t )2 + ··· + (Sdt )2 is the sub-fractional Bessel process.

Key words: sub-fractional Brownian motion, Malliavin calculus, sub-fractional Bessel processes, chaos expansion

中图分类号: 

  • 60G18