Laslett´s transform for the Boolean model in Rd

Title:

Laslett´s transform for the Boolean model in Rd

Creator:

Černý, Rostislav

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:5602acd8-34b3-4a28-9232-da886d5bd75b
uuid:5602acd8-34b3-4a28-9232-da886d5bd75b

Subject:

Boolean model and Laslett´s transform

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Consider a stationary Boolean model X with convex grains in Rd and let any exposed lower tangent point of X be shifted towards the hyperplane N0={x∈Rd:x1=0} by the length of the part of the segment between the point and its projection onto the N0 covered by X. The resulting point process in the halfspace (the Laslett's transform of X) is known to be stationary Poisson and of the same intensity as the original Boolean model. This result was first formulated for the planar Boolean model (see N. Cressie \cite{Cressie}) although the proof based on discretization is partly heuristic and not complete. Starting from the same idea we present a rigorous proof in the d-dimensional case. As a technical tool equivalent characterization of vague convergence for locally finite integer valued measures is formulated. Another proof based on the martingale approach was presented by A. D. Barbour and V. Schmidt \cite{barb+schm}.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

[569]-584

Source:

Kybernetika | 2006 Volume:42 | Number:5

Harvested from:

CDK

Metadata only:

false