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Local hitting and conditioning in symmetric interval partitions

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  • Kallenberg, Olav

Abstract

By a symmetric interval partition we mean a perfect, closed random set [Xi] in [0,1] of Lebesgue measure 0, such that the lengths of the connected components of [Xi]c occur in random order. Such sets are analogous to the regenerative sets on , and in particular there is a natural way to define a corresponding local time random measure [xi] with support [Xi]. In this paper, the author's recently developed duality theory is used to construct versions of the Palm distributions Qx of [xi] with attractive continuity and approximation properties. The results are based on an asymptotic formula for hitting probabilities and a delicate construction and analysis of conditional densities.

Suggested Citation

  • Kallenberg, Olav, 2001. "Local hitting and conditioning in symmetric interval partitions," Stochastic Processes and their Applications, Elsevier, vol. 94(2), pages 241-270, August.
    • Handle: RePEc:eee:spapps:v:94:y:2001:i:2:p:241-270
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