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The self-intersections of a Gaussian random field

Author

Listed:
  • Zhang, Rongmao
  • Lin, Zhengyan

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.

Suggested Citation

  • Zhang, Rongmao & Lin, Zhengyan, 2006. "The self-intersections of a Gaussian random field," Stochastic Processes and their Applications, Elsevier, vol. 116(9), pages 1294-1318, September.
    • Handle: RePEc:eee:spapps:v:116:y:2006:i:9:p:1294-1318
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    References listed on IDEAS

    as
    1. Csörgo, Miklós & Lin, Zheng-Yan & Shao, Qi-Man, 1995. "On moduli of continuity for local times of Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 58(1), pages 1-21, July.
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