ON INTERSECTIONS OF INDEPENDENT NONDEGENERATE DIFFUSION PROCESSES

doi:10.1016/S0252-9602(13)60132-0

数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (1): 141-161.doi: 10.1016/S0252-9602(13)60132-0

ON INTERSECTIONS OF INDEPENDENT NONDEGENERATE DIFFUSION PROCESSES

陈振龙

College of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China

收稿日期:2012-09-20 修回日期:2013-02-25 出版日期:2014-01-20 发布日期:2014-01-20
基金资助:
The research was supported by National Natural Science Foundation of China (11371321), Zhejiang Provincial Natural Science Foundation of China (Y6100663), the Key Research Base of Humanities and Social Sciences of Zhejiang Provincial High Education Talents (Statistics of Zhejiang Gongshang University).

ON INTERSECTIONS OF INDEPENDENT NONDEGENERATE DIFFUSION PROCESSES

CHEN Zhen-Long

College of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China

Received:2012-09-20 Revised:2013-02-25 Online:2014-01-20 Published:2014-01-20
Supported by:
The research was supported by National Natural Science Foundation of China (11371321), Zhejiang Provincial Natural Science Foundation of China (Y6100663), the Key Research Base of Humanities and Social Sciences of Zhejiang Provincial High Education Talents (Statistics of Zhejiang Gongshang University).

摘要/Abstract

摘要：

Let X⁽¹⁾ = {X⁽¹⁾(s), s ∈ R₊} and X⁽²⁾ = {X⁽²⁾(t), t ∈ R₊} be two inde-pendent nondegenerate diffusion processes with values in R^d. The existence and fractal dimension of intersections of the sample paths of X⁽¹⁾ and X⁽²⁾ are studied. More gener-ally, let E₁, E₂ ⊆ (0, ∞) and F ⊂ R^d be Borel sets. A necessary condition and a sufficient condition for P{X⁽¹⁾(E₁) ∩X⁽²⁾(E₂) ∩F 6≠Φ} > 0 are proved in terms of the Bessel-Riesz type capacity and Hausdorff measure of E₁×E₂×F in the metric space (R₊×R₊×R^d, ρ), where ρ is an unsymmetric metric defined in R₊ ×R₊ ×R^d. Under reasonable conditions, results resembling those of Browian motion are obtained.

关键词: intersection, diffusion processes, hitting probability, polar set, Hausdorff dimension

Abstract:

Key words: intersection, diffusion processes, hitting probability, polar set, Hausdorff dimension

中图分类号:

60G15

陈振龙. ON INTERSECTIONS OF INDEPENDENT NONDEGENERATE DIFFUSION PROCESSES[J]. 数学物理学报(英文版), 2014, 34(1): 141-161.

CHEN Zhen-Long. ON INTERSECTIONS OF INDEPENDENT NONDEGENERATE DIFFUSION PROCESSES[J]. Acta mathematica scientia,Series B, 2014, 34(1): 141-161.

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ON INTERSECTIONS OF INDEPENDENT NONDEGENERATE DIFFUSION PROCESSES

ON INTERSECTIONS OF INDEPENDENT NONDEGENERATE DIFFUSION PROCESSES

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