2008/12/23 by Mikhail Gordin, Gordin, Mikhail
Decision Sciences · Mathematics · #Applied mathematics #Discrete mathematics #Invertible matrix #Limit (mathematics) #Local martingale #Markov Chains and Monte Carlo Methods #Martingale (probability theory) #Martingale difference sequence #Mathematical analysis #Mathematics #Probability and Risk Models #Pure mathematics #Random field #Representation (politics) #Sequence (biology) #Statistics #Stochastic processes and statistical mechanics #math.PR #msc:60F99 #msc:60G60
paper · pdf · doi:10.48550/arxiv.0812.4414
published in arXiv (Cornell University) (Cornell University) · 20 pages; http://www.esi.ac.at/Preprint-shadows/esi2069/html
arxiv created 2008/12/23 · openalex publication_date 2008/12/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A stationary random sequence admits under some assumptions a representation as the sum of two others: one of them is a martingale difference sequence, and another 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 non-invertible probability preserving transformations. In this representation summands of mixed type appear which behave with respect to some groupof directions of the parameter space as reversed multiparameter martingale differences (in the sense of one of several known definitions) while they look as coboundaries relative to the other directions. Applications to limit theorems will be published elsewhere.