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Feb 2000 Asymptotic behaviour for interacting diffusion processes with space-time random birth
Begoña Fernández, Sylvie Méléard
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Bernoulli 6(1): 91-111 (Feb 2000).


We study the asymptotic behaviour of a system of interacting particles with space-time random birth. We have propagation of chaos and obtain the convergence of the empirical measures, when the size of the system tends to infinity. Then we show the convergence of the fluctuations, considered as cadlag processes with values in a weighted Sobolev space, to an Ornstein-Uhlenbeck process, the solution of a generalized Langevin equation. The tightness is proved by using a Hilbertian approach. The uniqueness of the limit is obtained by considering it as the solution of an evolution equation in a greater Banach space. The main difficulties are due to the unboundedness of the operators appearing in the semimartingale decomposition.


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Begoña Fernández. Sylvie Méléard. "Asymptotic behaviour for interacting diffusion processes with space-time random birth." Bernoulli 6 (1) 91 - 111, Feb 2000.


Published: Feb 2000
First available in Project Euclid: 22 April 2004

zbMATH: 0965.60065
MathSciNet: MR2001I:60167

Keywords: convergence of fluctuations , interacting particle systems , propagation of chaos , space-time random birth

Rights: Copyright © 2000 Bernoulli Society for Mathematical Statistics and Probability

Vol.6 • No. 1 • Feb 2000
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