Abstract
We consider the problem of finding conditions under which an \(\alpha\)-coupling is possible for several random variables \(X_1,X_2,\ldots,X_k\) with a finite or countably infinite range of values and with given probability distributions, i.e., the possibility of constructing a joint distribution of these random variables such that \(\Pr\{X_1=X_2=\ldots=X_k\}=\alpha\).
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Prelov, V.V., Coupling of Probability Distributions and an Extremal Problem for the Divergence, Probl. Peredachi Inf., 2015, vol. 51, no. 2, pp. 114–121 [Probl. Inf. Transm. (Engl. Transl.), 2015, vol. 51, no. 2, pp. 192–199]. https://doi.org/10.1134/S003294601502009X
Zhang, Z., Estimating Mutual Information via Kolmogorov Distance, IEEE Trans. Inform. Theory, 2007, vol. 53, no. 9, pp. 3280–3282. https://doi.org/10.1109/TIT.2007.903122
Sason, I., Entropy Bounds for Discrete Random Variables via Maximal Coupling, IEEE Trans. Inform. Theory, 2013, vol. 59, no. 11, pp. 7118–7131. https://doi.org/10.1109/TIT.2013.2274515
Strassen, V., The Existence of Probability Measures with Given Marginals, Ann. Math. Statist., 1965, vol. 36, no. 2, pp. 423–439. https://doi.org/10.1214/aoms/1177700153
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Translated from Problemy Peredachi Informatsii, 2022, Vol. 58, No. 4, pp. 6–12. https://doi.org/10.31857/S0555292322040027
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Prelov, V. Coupling of Several Random Variables. Probl Inf Transm 58, 300–305 (2022). https://doi.org/10.1134/S0032946022040020
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DOI: https://doi.org/10.1134/S0032946022040020