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28 March 2024
 
  » arxiv » 0711.0017

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On fractional Brownian motion limits in one dimensional nearest-neighbor symmetric simple exclusion
Magda Peligrad ; Sunder Sethuraman ;
Date 31 Oct 2007
AbstractA well-known result with respect to the one dimensional nearest-neighbor symmetric simple exclusion process is the convergence to fractional Brownian motion with Hurst parameter 1/4, in the sense of finite-dimensional distributions, of the subdiffusively rescaled current across the origin, and the subdiffusively rescaled tagged particle position.
The purpose of this note is to improve this convergence to a functional central limit theorem, with respect to the uniform topology, and so complete the solution to a conjecture in the literature with respect to simple exclusion processes.
Source arXiv, 0711.0017
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