On the almost sure central limit theorem for a class of $Z^d$-actions.
Gordin, Mikhail ; Weber, Michel
HAL, hal-00129654 / Harvested from HAL
Text on HAL
As an extension of earlier papers on stationary sequences, a concept of weak dependence for strictly stationary random fields is introduced in terms of so-called homoclinic transformations. Under assumptions made within the framework of this concept a form of the almost sure central limit theorem (ASCLT) is established for random fields arising from a class of algebraic $zd-$actions on compact abelian groups. As an auxiliary result, the central limit theorem is proved via Ch. Stein's method. The next stage of the proof includes some estimates which are specific for ASCLT. Both steps are based on making use of homoclinic transformations.
Publié le : 2002-07-05
Classification:  "Almost sure central limit theorem,  homoclinic transformations,  Almost sure central limit theorem,  homoclinic transformations",  28D99,  [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM] 
@article{hal-00129654,
     author = {Gordin, Mikhail and Weber, Michel},
     title = {On the almost sure central limit theorem for a class of $Z^d$-actions.},
     journal = {HAL},
     volume = {2002},
     number = {0},
     year = {2002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00129654}
}

Gordin, Mikhail; Weber, Michel. On the almost sure central limit theorem for a class of $Z^d$-actions.. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00129654/