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A central limit theorem for D(A)-valued processes

Author

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  • Bass, Richard F.
  • Pyke, Ronald

Abstract

Let D(A) be the space of set-indexed functions that are outer continuous with inner limits, a generalization of D[0, 1]. This paper proves a central limit theorem for triangular arrays of independent D(A) valued random variables. The limit processes are not restricted to be Gaussian, but can be quite general infinitely divisible processes. Applications of the theorem include construction of set-indexed Lévy processes and a unified central limit theorem for partial sum processes and generalized empirical processes. Results obtained are new even for the D[0, 1] case.

Suggested Citation

  • Bass, Richard F. & Pyke, Ronald, 1987. "A central limit theorem for D(A)-valued processes," Stochastic Processes and their Applications, Elsevier, vol. 24(1), pages 109-131, February.
    • Handle: RePEc:eee:spapps:v:24:y:1987:i:1:p:109-131
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    Cited by:

    1. Dalang, Robert C. & Khoshnevisan, Davar, 2004. "Recurrent lines in two-parameter isotropic stable Lévy sheets," Stochastic Processes and their Applications, Elsevier, vol. 114(1), pages 81-107, November.

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