Convergence Concepts and Limit Theorems

  • D. J. Daley
  • D. Vere-Jones
Part of the Springer Series in Statistics book series (SSS)


When random measures and point processes are regarded as probability measures on the appropriate c.s.m.s. \( {\hat M_X}\) or \( {\hat N_X}\), they may be associated with concepts of both weak and strong convergence of measures on a metric space. In this chapter we examine these concepts more closely, finding necessary and sufficient conditions for weak convergence, relating this concept to other possible definitions of convergence, and applying it to some near-classical questions concerning the convergence of superpositions, thinnings, and translations of point processes.


Limit Theorem Poisson Process Point Process Weak Convergence Random Measure 
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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • D. J. Daley
    • 1
  • D. Vere-Jones
    • 2
  1. 1.Department of Statistics Institute for Advanced StudyAustralian National UniversityCanberraAustralia
  2. 2.Department of StatisticsVictoria UniversityWellingtonNew Zealand

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