The self-intersections of a Gaussian random field

Rongmao Zhang and Zhengyan Lin

Stochastic Processes and their Applications, 2006, vol. 116, issue 9, 1294-1318

Abstract: Let X(t) be an non-deterministic Gaussian field. In this paper, the sufficient conditions for existence of the k-multiple points, the Hausdorff measure and the Hausdorff dimension for the k-multiple times set {(t1,t2,...,tk):X(t1)=X(t2)=...=X(tk) for distinct t1,t2,...,tk} and the local times of the process Y(T)={X(t2)-X(t1),...,X(tk)-X(tk-1)} are evaluated.

Keywords: 60G17; 60J65; 60F15; Hausdorff; measure; Multiple; point; k-Multiple; times; set; Local; time; Gaussian; random; field (search for similar items in EconPapers)
Date: 2006
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