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An extension of the basic Palm measure correspondence
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  • Published: May 2000

An extension of the basic Palm measure correspondence

  • Olav Kallenberg1 

Probability Theory and Related Fields volume 117, pages 113–131 (2000)Cite this article

Abstract.

The notion of Palm measure provides a one-to-one correspondence between the distributions of simple, stationary point processes on ℝ with finite intensity and those of stationary sequences of positive random variables with finite mean. Here we extend this result to any stationary random measures on ℝ, using a new notion of spacing measure based on an elementary measure inversion. Our approach is symmetric, in the sense that an iteration of the spacing measure construction leads back to the original distribution. The classical results for point processes arise as simple special cases.

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Authors and Affiliations

  1. Department of Mathematics, Auburn University, 218 Parker Hall, Auburn, AL 36849-5310, USA. e-mail: olavk@mail.auburn.edu, , , , , , US

    Olav Kallenberg

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  1. Olav Kallenberg
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Received: 30 September 1998 / Revised version: 9 June 1999 / Published online: 30 March 2000

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Kallenberg, O. An extension of the basic Palm measure correspondence. Probab Theory Relat Fields 117, 113–131 (2000). https://doi.org/10.1007/s004400050267

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  • Issue Date: May 2000

  • DOI: https://doi.org/10.1007/s004400050267

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Keywords

  • Stationary Point
  • Point Process
  • Finite Intensity
  • Spacing Measure
  • Classical Result
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