## Abstract

Consider a population of infinitesimally small frogs on the real line. Initially the frogs on the positive half-line are dormant while those on the negative half-line are awake and move according to the heat flow. At the interface, the incoming wake frogs try to wake up the dormant frogs and succeed with a probability proportional to their amount among the total amount of involved frogs at the specific site. Otherwise, the incoming frogs also fall asleep. This frog model is a special case of the infinite rate symbiotic branching process on the real line with different motion speeds for the two types. We construct this frog model as the limit of approximating processes and compute the structure of jumps. We show that our frog model can be described by a stochastic partial differential equation on the real line with a jump type noise.

Original language | English |
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Pages (from-to) | 847-883 |

Number of pages | 37 |

Journal | Annales de l'institut Henri Poincare (B) Probability and Statistics |

Volume | 56 |

Issue number | 2 |

DOIs | |

State | Published - 2020 |

## Keywords

- Frog model
- Infinite rate branching
- Mutually catalytic branching
- Stochastic partial differential equation
- Symbiotic branching

## ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty