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Estimation du contour discontinu d’un processus ponctuel sur le plan. (Estimation of the discontinuous contour of a point process in the plane). (French) Zbl 0652.62086

Summary: The spectrum of a point process is supposed to be defined on the plane by: \(\{\) (x,y)\(\in {\mathbb{R}}^ 2:\) \(0\leq x\leq 1\); \(0<y<\max (\phi (x);\phi (x\)-))\(\}\) where \(\phi\) is a right continuous with left-hand limits function. We study sufficient conditions of stochastic convergence to \(\phi\) in the L p-norm or in the Skorokhod topology of some estimates. The limit law is found in a particular case. We also give estimates of jumps and of their sizes.

MSC:

62M09 Non-Markovian processes: estimation
62E20 Asymptotic distribution theory in statistics
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
62G05 Nonparametric estimation
60F25 \(L^p\)-limit theorems
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