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.
Author information
Authors and Affiliations
Additional information
Received: 30 September 1998 / Revised version: 9 June 1999 / Published online: 30 March 2000
Rights and permissions
About this article
Cite this article
Kallenberg, O. An extension of the basic Palm measure correspondence. Probab Theory Relat Fields 117, 113–131 (2000). https://doi.org/10.1007/s004400050267
Issue Date:
DOI: https://doi.org/10.1007/s004400050267
Keywords
- Stationary Point
- Point Process
- Finite Intensity
- Spacing Measure
- Classical Result