Finite system scheme for mutually catalytic branching with infinite branching rate

Leif DÖRing, Achim Klenke, Leonid Mytnik

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)3113-3152
Number of pages40
JournalAnnals of Applied Probability
Issue number5
StatePublished - Oct 2017


  • Finite systems scheme
  • Interacting diffusions
  • Meanfield limit
  • Mutually catalytic branching

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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