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Central limit theorems for point processes

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  • Ivanoff, Gail

Abstract

The problem considered is the existence of central limit theorems for the sequence of random measures {MK} on n where , and NK is renormalization of a point process N on n defined by [is proportional to].Various mixing conditions are defined and sufficient conditions are given for the existence of each of the following three types of central limit theorem: 1. (a) Convergence of MK(A) to a normal random variable for specified A [subset, double equals] n. 2. (b) Convergence ofMK(·) to a generalized Gaussian random field defined on n. 3. (c) Weak convergence ofXK(t1,...,tn)=MK((0,t1]x...x(l),tn]) in the Skorokhod topo logy on[0,T]n to then-dimensional Wiener process.

Suggested Citation

  • Ivanoff, Gail, 1982. "Central limit theorems for point processes," Stochastic Processes and their Applications, Elsevier, vol. 12(2), pages 171-186, March.
    • Handle: RePEc:eee:spapps:v:12:y:1982:i:2:p:171-186
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    Cited by:

    1. Kutoyants, Yu. A. & Liese, F., 1998. "Estimation of linear functionals of Poisson processes," Statistics & Probability Letters, Elsevier, vol. 40(1), pages 43-55, September.
    2. Zhang, Tonglin & Zhuang, Run, 2017. "Testing proportionality between the first-order intensity functions of spatial point processes," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 72-82.
    3. Zhang, Tonglin & Mateu, Jorge, 2019. "Substationarity for spatial point processes," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 22-36.
    4. Heinrich, Lothar, 2018. "Brillinger-mixing point processes need not to be ergodic," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 31-35.

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