Central limit theorems for point processes

Gail Ivanoff

Stochastic Processes and their Applications, 1982, vol. 12, issue 2, 171-186

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.

Keywords: Point; process; probability; generating; functional; factorial; moment; density; function; central; limit; theorem; Wiener; process; mixing; Poison; cluster; process; Laplace; transform; factorial; cumulant; density; function; generalised; Gaussian; random; field; Skorokhod; topology (search for similar items in EconPapers)
Date: 1982
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Citations: View citations in EconPapers (5)

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