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.
In: Communications on Pure and Applied Mathematics, Vol. 60, No. 7, 07.2007, p. 1056-1080.Research output: Contribution to journal › Article
}
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
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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 -