An Introduction to the Theory of Point Processes pp 131-175 | Cite as

# Convergence Concepts and Limit Theorems

Chapter

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.

## Keywords

Limit Theorem Poisson Process Point Process Weak Convergence Random Measure
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© Springer 2008