An alternative proof of the uniqueness of martingale-coboundary decomposition of strictly stationary processes

Takehiko Morita

Commentationes Mathematicae Universitatis Carolinae (2019)

  • Volume: 60, Issue: 3, page 415-419
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Morita, Takehiko. "An alternative proof of the uniqueness of martingale-coboundary decomposition of strictly stationary processes." Commentationes Mathematicae Universitatis Carolinae 60.3 (2019): 415-419. <http://eudml.org/doc/294494>.

@article{Morita2019,
abstract = {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.},
author = {Morita, Takehiko},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {strictly stationary process; martingale-coboundary decomposition},
language = {eng},
number = {3},
pages = {415-419},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {An alternative proof of the uniqueness of martingale-coboundary decomposition of strictly stationary processes},
url = {http://eudml.org/doc/294494},
volume = {60},
year = {2019},
}

TY - JOUR
AU - Morita, Takehiko
TI - An alternative proof of the uniqueness of martingale-coboundary decomposition of strictly stationary processes
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2019
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 60
IS - 3
SP - 415
EP - 419
AB - 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.
LA - eng
KW - strictly stationary process; martingale-coboundary decomposition
UR - http://eudml.org/doc/294494
ER -

References

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  1. Billingsley P., Ergodic Theory and Information, John Wiley & Sons, New York, 1965. MR0192027
  2. Hall P., Heyde C. C., Martingale Limit Theory and Its Application, Probability and Mathematical Statistics, Academic Press, New York, 1980. Zbl0462.60045MR0624435
  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. MR1173752
  4. Volný D., 10.1016/0304-4149(93)90037-5, Stochastic Process. Appl. 44 (1993), no. 1, 41–74. MR1198662DOI10.1016/0304-4149(93)90037-5
  5. Walters P., 10.1007/978-1-4612-5775-2, Graduate Texts in Mathematics, 79, Springer, New York, 1982. Zbl0958.28011MR0648108DOI10.1007/978-1-4612-5775-2

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