Convergence Concepts and Limit Theorems

Part of the Probability and Its Applications book series (PIA)

When random measures and point processes are regarded as probability measures on the appropriate c.s.m.s. M# x or 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 2008

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