Advances in Applied Probability

Comparisons and asymptotics for empty space hazard functions of germ-grain models

Günter Last and Ryszard Szekli

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Abstract

We study stochastic properties of the empty space for stationary germ-grain models in Rd; in particular, we deal with the inner radius of the empty space with respect to a general structuring element which is allowed to be lower dimensional. We consider Poisson cluster and mixed Poisson germ-grain models, and show in several situations that more variability results in stochastically greater empty space in terms of the empty space hazard function. Furthermore, we study the asymptotic behaviour of the empty space hazard functions at 0 and at ∞.

Article information

Source
Adv. in Appl. Probab., Volume 43, Number 4 (2011), 943-962.

Dates
First available in Project Euclid: 16 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.aap/1324045693

Digital Object Identifier
doi:10.1239/aap/1324045693

Mathematical Reviews number (MathSciNet)
MR2867940

Zentralblatt MATH identifier
1238.60015

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 60G55: Point processes

Keywords
Germ-grain model empty space hazard relative distance point process Poisson cluster process mixed Poisson process hazard rate ordering

Citation

Last, Günter; Szekli, Ryszard. Comparisons and asymptotics for empty space hazard functions of germ-grain models. Adv. in Appl. Probab. 43 (2011), no. 4, 943--962. doi:10.1239/aap/1324045693. https://projecteuclid.org/euclid.aap/1324045693


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