Fluctuations and moderate deviations for a catalytic Fleming–Viot branching system in nonequilibrium

Abstract

We consider fluctuations and moderate deviations of the empirical fields for a catalytic Fleming–Viot branching system in nonequilibrium. We proved that for some independent initial distribution, the fluctuation process of the empirical fields is governed by an Ornstein–Uhlenbeck process whose drift term is a linear operator associated with a catalyst. Furthermore, we establish the large deviation principle corresponding to the fluctuation. We develop a technique to estimate the exponential moments for the Sobolev norms of the empirical fluctuation fields via the spectrum of the Laplace operator and the exponential inequality of martingales. The estimates of the exponential moments play a crucial role in this paper.