Limit theorems for point processes and their functionals
نویسندگان
چکیده
منابع مشابه
Limit theorems for geometric functionals of Gibbs point processes
Observations are made on a point process Ξ in R in a window Qλ of volume λ. The observation, or ‘score’ at a point x, here denoted ξ(x, Ξ), is a function of the points within a random distance of x. When the input Ξ is a Poisson or binomial point process, the large λ limit theory for the total score ∑ x∈Ξ∩Qλ ξ(x, Ξ ∩Qλ), when properly scaled and centered, is well understood. In this paper we es...
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Given a Gibbs point process P on R having a weak enough potential Ψ, we consider the random measures μλ := P x∈P∩Qλ ξ(x,P ∩Qλ)δx/λ1/d , where Qλ := [−λ /2, λ/2] is the volume λ cube and where ξ(·, ·) is a translation invariant stabilizing functional. Subject to Ψ satisfying a localization property and translation invariance, we establish weak laws of large numbers for λ−1μλ(f), f a bounded test...
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In this article, we consider a sequence (Nn)n≥1 of point processes, whose points lie in a subset E of R\{0}, and satisfy an asymptotic independence condition. Our main result gives some necessary and sufficient conditions for the convergence in distribution of (Nn)n≥1 to an infinitely divisible point process N . As applications, we discuss the exceedance processes and point processes based on r...
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1986
ISSN: 0025-5645
DOI: 10.2969/jmsj/03830543