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.
ASJC Scopus subject areas
- Applied Mathematics