It is known that under some conditions, a stationary random sequence admits a representation as a sum of two sequences: one of them is a martingale difference sequence, and another one is a so-called coboundary. Such a representation can be used for proving some limit theorems by means of the martingale approximation. A multivariate version of such a decomposition is presented in the paper for a class of random fields generated by several commuting, noninvertible, probability preserving transformations In this representation, summands of mixed type appear, which behave with respect to some group of directions of the parameter space as reversed rnultiparameter martingale differences (in the sense of one of several known definitions), while they look as coboundaries relative to other directions. Applications to limit theorems will be published elsewhere. Bibliography: 14 titles.
Russia Parameter Space Limit Theorem Random Field Random Sequence
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.
A. K. Basu and C. C. Y. Dorea, “On functional central limit theorem for stationary martingale random fields,” Acta Math. Acad. Sci. Hangar., 33, 307–316 (1979).MATHCrossRefMathSciNetGoogle Scholar
M. Gordin and M. Weber, “On the central limit theorem for a class of multivariate actions” (in preparation).Google Scholar
N. Maigret, “Théorème de limite centrale fonctionnel pour une chaîne de Markov récurrente au sens de Harris et positive,” Ann. Inst. H. Poincaré, Sect. B (N.S.), 14, 425–440 (1978).MATHMathSciNetGoogle Scholar