Abstract
For a regenerative process X with associated local time random measure ξ, the distribution relative to some fixed times has a simple description in terms of the excursion kernel (νr) and the Palm distributions Q t with respect to ξ. Under suitable regularity conditions on ξ, the Q t admit versions with strong continuity and regularity properties. Using the latter versions, we may establish some local invariance and mixing properties of X and show that the multivariate Palm distributions can be approximated by ordinary conditional distributions.
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Received: 10 July 2001 / Revised version: 17 April 2002 / Published online: 10 September 2002
Mathematics Subject Classification (2000): 60G57, 60J55, 60K05
Key words or phrases: Palm measures – Local time – Excursion law – Conditional distributions – Hitting probabilities – Mixing – Local invariance – Exchangeability
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Kallenberg, O. Palm distributions and local approximation of regenerative processes. Probab Theory Relat Fields 125, 1–41 (2003). https://doi.org/10.1007/s004400200218
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DOI: https://doi.org/10.1007/s004400200218
Keywords
- Regenerative Process
- Local Approximation
- Palm Distribution