|
Zapiski Nauchnykh Seminarov POMI, 2015, Volume 441, Pages 239–262
(Mi znsl6236)
|
|
|
|
This article is cited in 15 scientific papers (total in 15 papers)
A functional CLT for fields of commuting transformations via martingale approximation
Ch. Cunya, J. Dedeckerb, D. Volnýc a Laboratoire MAS, Centrale-Supelec, Grande Voie des Vignes, 92295 Chatenay-Malabry cedex, France
b Laboratoire MAP5 (UMR 8145), Université Paris Descartes, Sorbonne Paris Cité, 45 rue des Saints Pères, 75270 Paris Cedex 06, France
c Laboratoire de Mathématiques Raphaël Salem (UMR 6085), Université de Rouen, Avenue de l'Universit, BP.12 76801 Saint-Etienne du Rouvray, France
Abstract:
We consider a field $f\circ T^{i_1}_1\circ\dots\circ T_d^{i_d}$, where $T_1,\dots,T_d$ are completely commuting transformations in the sense of Gordin. If one of these transformations is ergodic, we give sufficient conditions in the spirit of Hannan under which the partial sum process indexed by quadrants converges in distribution to a Brownian sheet. The proof combines a martingale approximation approach with a recent CLT for martingale random fields due to Volný. We apply our results to completely commuting endomorphisms of the $m$-torus. In that case, the conditions can be expressed in terms of the $L^2$-modulus of continuity of $f$.
Key words and phrases:
random fields, reverse martingales, endomorphisms of the torus.
Received: 12.10.2015
Citation:
Ch. Cuny, J. Dedecker, D. Volný, “A functional CLT for fields of commuting transformations via martingale approximation”, Probability and statistics. Part 22, Zap. Nauchn. Sem. POMI, 441, POMI, St. Petersburg, 2015, 239–262; J. Math. Sci. (N. Y.), 219:5 (2016), 765–781
Linking options:
https://www.mathnet.ru/eng/znsl6236 https://www.mathnet.ru/eng/znsl/v441/p239
|
Statistics & downloads: |
Abstract page: | 151 | Full-text PDF : | 57 | References: | 36 |
|