1998 | OriginalPaper | Buchkapitel
Convergence Concepts and Limit Theorems
verfasst von : D. J. Daley, D. Vere-Jones
Erschienen in: An Introduction to the Theory of Point Processes
Verlag: Springer New York
Enthalten in: Professional Book Archive
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When random measures and point processes are regarded as probability measures on the appropriate c.s.m.s. % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmytayaaja % WaaSbaaSqaaiaadIfaaeqaaaaa!37DF!$$ {\hat M_X}$$ or % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmOtayaaja % WaaSbaaSqaaiaadIfaaeqaaaaa!37E0!$$ {\hat N_X}$$, 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.