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Stochastic Order and Attractiveness for Particle Systems with Multiple Births, Deaths and Jumps


 
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1. Title Title of document Stochastic Order and Attractiveness for Particle Systems with Multiple Births, Deaths and Jumps
 
2. Creator Author's name, affiliation, country Davide Borrello; Università di Milano and Universié de Rouen; Italy
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Stochastic order; attractiveness; interacting particle systems; epidemic model; multitype contact process
 
3. Subject Subject classification 60K35; 82C22
 
4. Description Abstract An approach to analyse the properties of a particle system is to compare it with different processes to understand when one of them is larger than other ones. The main technique for that is coupling, which may not be easy to construct. We give a characterization of stochastic order between different interacting particle systems in a large class of processes with births, deaths and jumps of many particles per time depending on the configuration in a general way: it consists in checking inequalities involving the transition rates. We construct explicitly the coupling that characterizes the stochastic order. As a corollary we get necessary and sufficient conditions for attractiveness. As an application, we first give the conditions on examples including reaction-diffusion processes, multitype contact process and conservative dynamics and then we improve an ergodicity result for an epidemic model.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Fondations Sciences Mathematiques de Paris; ANR grant BLAN07-218426
 
7. Date (YYYY-MM-DD) 2011-01-09
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/852
 
10. Identifier Digital Object Identifier 10.1214/EJP.v16-852
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 16
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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