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Keywords:
strictly stationary process; martingale-coboundary decomposition
strictly stationary process; martingale-coboundary decomposition
Summary:
P. Samek and D. Volný, in the paper ``Uniqueness of a martingale-coboundary decomposition of a stationary processes" (1992), showed the uniqueness of martingale-coboundary decomposition of strictly stationary processes. The original proof is given by reducing the problem to the ergodic case. In this note we give another proof without such reduction.
References:
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[2] Hall P., Heyde C. C.: Martingale Limit Theory and Its Application. Probability and Mathematical Statistics, Academic Press, New York, 1980. MR 0624435 | Zbl 0462.60045
[3] Samek P., Volný D.: Uniqueness of a martingale-coboundary decomposition of a stationary processes. Comment. Math. Univ. Carolin. 33 (1992), no. 1, 113–119. MR 1173752
[4] Volný D.: Approximating martingales and the central limit theorem for strictly stationary processes. Stochastic Process. Appl. 44 (1993), no. 1, 41–74. DOI 10.1016/0304-4149(93)90037-5 | MR 1198662
[5] Walters P.: An Introduction to Ergodic Theory. Graduate Texts in Mathematics, 79, Springer, New York, 1982. DOI 10.1007/978-1-4612-5775-2 | MR 0648108 | Zbl 0958.28011
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