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A limit theorem for quadratic fluctuations in symmetric simple exclusion
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Assing, Sigurd (2007) A limit theorem for quadratic fluctuations in symmetric simple exclusion. Stochastic Processes and their Applications, Vol.117 (No.6). pp. 766-790. doi:10.1016/j.spa.2006.10.005
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Official URL: http://dx.doi.org/10.1016/j.spa.2006.10.005
Abstract
We consider quadratic fluctuations V-epsilon(H) (eta(s)) = root epsilon Sigma(x is an element of Z) H(epsilon x)eta(s)(x)eta(s) (x + x(0)) in the centered symmetric simple exclusion process in dimension d = 1. Although the order of divergence of root E[(epsilon-2)(0) ds v(epsilon)(h) (eta(s))](2) is known to be epsilon(-3/2) if epsilon down arrow 0 the corresponding limit theorem was so far not explored. We now show that epsilon(3/2) integral(t epsilon)(0)(-2) ds V-epsilon(H) (eta(s)) converges in law to a non-Gaussian singular functional of an infinite-dimensional Ornstein-Uhlenbeck process. Despite the singularity of the limiting functional we find enough structure to conclude that it is continuous but not a martingale in t. We remark that in symmetric exclusion in dimensions d >= 3 the corresponding functional central limit theorem is known to produce Gaussian martingales in t. The case d = 2 remains open. (C) 2006 Elsevier B.V. All rights reserved.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science > Statistics | ||||
| Journal or Publication Title: | Stochastic Processes and their Applications | ||||
| Publisher: | Elsevier Science BV | ||||
| ISSN: | 0304-4149 | ||||
| Official Date: | June 2007 | ||||
| Dates: |
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| Volume: | Vol.117 | ||||
| Number: | No.6 | ||||
| Number of Pages: | 25 | ||||
| Page Range: | pp. 766-790 | ||||
| DOI: | 10.1016/j.spa.2006.10.005 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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