Electronic Journal of Probability
- Electron. J. Probab.
- Volume 16 (2011), paper no. 4, 106-151.
Stochastic Order and Attractiveness for Particle Systems with Multiple Births, Deaths and Jumps
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.
Electron. J. Probab., Volume 16 (2011), paper no. 4, 106-151.
Accepted: 9 January 2011
First available in Project Euclid: 1 June 2016
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Borrello, Davide. Stochastic Order and Attractiveness for Particle Systems with Multiple Births, Deaths and Jumps. Electron. J. Probab. 16 (2011), paper no. 4, 106--151. doi:10.1214/EJP.v16-852. https://projecteuclid.org/euclid.ejp/1464820173