Finite system scheme for infinite rate mutually catalytic branching with infinite branching rate
Abstract
For many stochastic diffusion processes with mean field interaction, convergence of the rescaled total mass processes towards a diffusion process is known. Here we show convergence of the socalled finite system scheme for interacting jumptype processes known as mutually catalytic branching processes with infinite branching rate. Due to the lack of second moments the rescaling of time is different from the finite rate mutually catalytic case. The limit of rescaled total mass processes is identified as the finite rate mutually catalytic branching diffusion. The convergence of rescaled processes holds jointly with convergence of coordinate processes, whereas the latter converge at a different time scale.
 Publication:

arXiv eprints
 Pub Date:
 October 2015
 arXiv:
 arXiv:1510.01154
 Bibcode:
 2015arXiv151001154D
 Keywords:

 Mathematics  Probability;
 Primary 60K35;
 Secondary 60J80;
 60J60;
 60J75;
 60F05;
 60H20