Functional central limit theorems for seeds in a linear birth and growth model

Volume 43 / 2016

A. Dziwisz, W. Szczotka Applicationes Mathematicae 43 (2016), 1-24 MSC: Primary 60G55; Secondary 60F17. DOI: 10.4064/am2283-2-2016 Published online: 2 June 2016

Abstract

A problem of heredity of mixing properties ($\alpha $-mixing, $\beta $-mixing and $\rho $-mixing) from a stationary point process on $\mathbb R\times \mathbb R_{+}$ to a sequence of some of its points called ‘seeds’ is considered. Next, using the mixing properties, several versions of functional central limit theorems for the distances between seeds and the process of the number of seeds are obtained.

Authors

  • A. DziwiszInstitute of Mathematics
    University of Wrocław
    50-384 Wroclaw, Poland
  • W. SzczotkaInstitute of Mathematics
    University of Wrocław
    50-384 Wrocław, Poland
    e-mail

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