Journal of Applied Probability

On the growth of the one-dimensional reverse immunization contact processes

A. Tzioufas

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Abstract

We are concerned with the variation of the supercritical nearest-neighbours contact process such that first infection occurs at a lower rate; it is known that the process survives with positive probability. Regarding the rightmost infected of the process started from one site infected and conditioned to survive, we specify a sequence of space-time points at which its behaviour regenerates and, thus, obtain the corresponding strong law and central limit theorem. We also extend complete convergence in this case.

Article information

Source
J. Appl. Probab., Volume 48, Number 3 (2011), 611-623.

Dates
First available in Project Euclid: 23 September 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1316796902

Digital Object Identifier
doi:10.1239/jap/1316796902

Mathematical Reviews number (MathSciNet)
MR2884803

Zentralblatt MATH identifier
1230.60104

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82C22: Interacting particle systems [See also 60K35]

Keywords
Contact process Kuczek-type argument

Citation

Tzioufas, A. On the growth of the one-dimensional reverse immunization contact processes. J. Appl. Probab. 48 (2011), no. 3, 611--623. doi:10.1239/jap/1316796902. https://projecteuclid.org/euclid.jap/1316796902


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