## Abstract

We construct a mutually catalytic branching process on a countable site space with infinite "branching rate". The finite rate mutually catalytic model, in which the rate of branching of one population at a site is proportional to the mass of the other population at that site, was introduced by Dawson and Perkins (Ann Probab 26(3):1088-1138, 1998). We show that our model is the limit for a class of models and in particular for the Dawson-Perkins model as the rate of branching goes to infinity. Our process is characterized as the unique solution to a martingale problem. We also give a characterization of the process as a weak solution of an infinite system of stochastic integral equations driven by a Poisson noise.

Original language | English |
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Pages (from-to) | 533-584 |

Number of pages | 52 |

Journal | Probability Theory and Related Fields |

Volume | 154 |

Issue number | 3-4 |

DOIs | |

State | Published - Dec 2012 |

## Keywords

- Duality
- Martingale problem
- Mutually catalytic branching
- Stochastic differential equations

## All Science Journal Classification (ASJC) codes

- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty