Acta mathematica scientia, Series B >
ON INTERSECTIONS OF INDEPENDENT NONDEGENERATE DIFFUSION PROCESSES
Received date: 2012-09-20
Revised date: 2013-02-25
Online 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).
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 Rd. 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 ⊂ Rd 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+×Rd, ρ), where ρ is an unsymmetric metric defined in R+ ×R+ ×Rd. Under reasonable conditions, results resembling those of Browian motion are obtained.
CHEN Zhen-Long . ON INTERSECTIONS OF INDEPENDENT NONDEGENERATE DIFFUSION PROCESSES[J]. Acta mathematica scientia, Series B, 2014 , 34(1) : 141 -161 . DOI: 10.1016/S0252-9602(13)60132-0
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