Abstract
AbstractWe 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. © 2006 Wiley Periodicals, Inc.
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