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October 2017 Finite system scheme for mutually catalytic branching with infinite branching rate
Leif Döring, Achim Klenke, Leonid Mytnik
Ann. Appl. Probab. 27(5): 3113-3152 (October 2017). DOI: 10.1214/17-AAP1277


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.


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Leif Döring. Achim Klenke. Leonid Mytnik. "Finite system scheme for mutually catalytic branching with infinite branching rate." Ann. Appl. Probab. 27 (5) 3113 - 3152, October 2017.


Received: 1 October 2015; Revised: 1 September 2016; Published: October 2017
First available in Project Euclid: 3 November 2017

zbMATH: 1379.60097
MathSciNet: MR3719954
Digital Object Identifier: 10.1214/17-AAP1277

Primary: 60K35
Secondary: 60F05 , 60H20 , 60J60 , 60J75 , 60J80

Keywords: Finite systems scheme , Interacting diffusions , meanfield limit , Mutually catalytic branching

Rights: Copyright © 2017 Institute of Mathematical Statistics


Vol.27 • No. 5 • October 2017
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