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Contiguity and LAN-property of sequences of Poisson processes. (English) Zbl 1274.60156
Summary: Using the concept of Hellinger integrals, necessary and sufficient conditions are established for the contiguity of two sequences of distributions of Poisson point processes with an arbitrary state space. The distribution of the logarithm of the likelihood ratio is shown to be infinitely divisible. The canonical measure is expressed in terms of the intensity measures. Necessary and sufficient conditions for the LAN-property are formulated in terms of the corresponding intensity measures.
MSC:
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
62B10 Statistical aspects of information-theoretic topics
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