### Abstract

We consider a jump-diffusion process describing a system of diffusing particles that upon contact with an obstacle (catalyst) die and are replaced by an independent offspring with position chosen according to a weighted average of the remaining particles. The obstacle is a bounded nonnegative function V (x) and the birth/death mechanism is similar to the Fleming-Viot critical branching. Since the mass is conserved, we prove a hydrodynamic limit for the empirical measure, identified as the solution to a generalized semilinear (reaction-diffusion) equation, with nonlinearity given by a quadratic operator. A large-deviation principle from the deterministic hydrodynamic limit is provided. The upper bound is given in any dimension, and the lower bound is proven for d = 1 and V bounded away from 0. An explicit formula for the rate function is provided via an Orlicz-type space.

Original language | English (US) |
---|---|

Pages (from-to) | 1056-1080 |

Number of pages | 25 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 60 |

Issue number | 7 |

DOIs | |

State | Published - Jul 2007 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**Large deviations for a catalytic fleming-viot branching system.** / Grigorescu, Ilie.

Research output: Contribution to journal › Article

*Communications on Pure and Applied Mathematics*, vol. 60, no. 7, pp. 1056-1080. https://doi.org/10.1002/cpa.20174

}

TY - JOUR

T1 - Large deviations for a catalytic fleming-viot branching system

AU - Grigorescu, Ilie

PY - 2007/7

Y1 - 2007/7

N2 - We consider a jump-diffusion process describing a system of diffusing particles that upon contact with an obstacle (catalyst) die and are replaced by an independent offspring with position chosen according to a weighted average of the remaining particles. The obstacle is a bounded nonnegative function V (x) and the birth/death mechanism is similar to the Fleming-Viot critical branching. Since the mass is conserved, we prove a hydrodynamic limit for the empirical measure, identified as the solution to a generalized semilinear (reaction-diffusion) equation, with nonlinearity given by a quadratic operator. A large-deviation principle from the deterministic hydrodynamic limit is provided. The upper bound is given in any dimension, and the lower bound is proven for d = 1 and V bounded away from 0. An explicit formula for the rate function is provided via an Orlicz-type space.

AB - We consider a jump-diffusion process describing a system of diffusing particles that upon contact with an obstacle (catalyst) die and are replaced by an independent offspring with position chosen according to a weighted average of the remaining particles. The obstacle is a bounded nonnegative function V (x) and the birth/death mechanism is similar to the Fleming-Viot critical branching. Since the mass is conserved, we prove a hydrodynamic limit for the empirical measure, identified as the solution to a generalized semilinear (reaction-diffusion) equation, with nonlinearity given by a quadratic operator. A large-deviation principle from the deterministic hydrodynamic limit is provided. The upper bound is given in any dimension, and the lower bound is proven for d = 1 and V bounded away from 0. An explicit formula for the rate function is provided via an Orlicz-type space.

UR - http://www.scopus.com/inward/record.url?scp=34249693097&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34249693097&partnerID=8YFLogxK

U2 - 10.1002/cpa.20174

DO - 10.1002/cpa.20174

M3 - Article

VL - 60

SP - 1056

EP - 1080

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 7

ER -