Uniform convergence in some limit theorems for multiple particle systems

[摘要] For n particles diffusing throughout R (or R-d), let eta(n,t)(A), A is an element of B, t greater than or equal to 0, be the random measure that counts the number of particles in A at time t. It is shown that for some basic models (Brownian particles with or without branching and diffusion with a simple interaction) the processes cesses {(eta(n,t)(phi) - E eta(n,t)(phi))/root n:t is an element of [O,M], phi is an element of C-L(alpha)(R)}, n is an element of N, converge in law uniformly in (t, phi). Previous results consider only convergence in law uniform in t but not in phi. The methods used are from empirical process theory. (C) 1997 Elsevier Science B.V.

[发布日期] 1997-12-01

[关键词] Brownian motion;distribution-valued processes;central limit theorem;empirical processes;Holder functions;particle systems