Finite system scheme for mutually catalytic branching with infinite branching rate. (English) Zbl 1379.60097

Döring, Leif; Klenke, Achim; Mytnik, Leonid

Ann. Appl. Probab. 27, No. 5, 3113-3152 (2017).

Summary: 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 so-called finite system scheme for interacting jump-type 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, where the latter converge at a different time scale.

MSC:

60K35	Interacting random processes; statistical mechanics type models; percolation theory
60J80	Branching processes (Galton-Watson, birth-and-death, etc.)
60J60	Diffusion processes
60J75	Jump processes (MSC2010)
60F05	Central limit and other weak theorems

Keywords:

finite systems scheme; interacting diffusions; meanfield limit; mutually catalytic branching