Modified Palm and Modified Time-Stationary Distributions for Random Measures and Applications
Masakiyo Miyazawa, Gert Nieuwenhuis · Data Archiving and Networked Services (DANS) · 1995
Palm distributions are known to be useful to obtain relations among various characteristics concerning stationary processes, in particular, arising in queueing theory.By assuming ergodicity, one can derive sample-path formulas from t hese relations.However, if ergodicity d o e s n o t hold, there has been a certain gap between the expectation and the sample-path formulas.This gap h a s recently been lled by i n troducing modi ed Palm distributions, which a l s o h a v e n i c e p h ysical interpretations.Under this setting, conditional expectation versions of relations such as Campbell's formula have been obtained, which can be expressed in terms of long-run sample averages.The main purpose of this paper is to generalize those formulas for the modi ed Palm distribution w ith respect to a stationary random measure.We a lso introduce a modi ed time-stationary distribution, and apply those modi ed distributions for characterizing the limit distributions of asymptotic stationary processes.