LARGE DEVIATIONS FOR THE OCCUPATION TIME FUNCTIONAL OF A POISSON SYSTEM OF INDEPENDENT BROWNIAN PARTICLES

Authors
DEUSCHEL JD WANG KM
Citation
Jd. Deuschel et Km. Wang, LARGE DEVIATIONS FOR THE OCCUPATION TIME FUNCTIONAL OF A POISSON SYSTEM OF INDEPENDENT BROWNIAN PARTICLES, Stochastic processes and their applications, 52(2), 1994, pp. 183-209
Citations number
15
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Stochastic processes and their applications → ACNP
ISSN journal
03044149
Volume
52
Issue
2
Year of publication
1994
Pages
183 - 209
Database
ISI
SICI code
0304-4149(1994)52:2<183:LDFTOT>2.0.ZU;2-B
Abstract
We study the large deviations and the central limit theorem for the oc cupation time functional of a Poisson system of independent Brownian p articles in R(d), extending the results of Cox and Griffeath (1984) to functional spaces. In the lower (recurrent) dimensions d = 1,2 we hav e critical orders T-1/2 and T/log T, whereas in higher (transient) dim ensions we have the usual order T. We give explicit expressions for th e corresponding rate functions and covariance functionals and derive s ome asymptotic microcanonical distributions.