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Characterization of distributions of Q-independent random variables on locally compact Abelian groups

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  • Myronyuk, Margaryta

Abstract

Let X be a second countable locally compact Abelian group. We prove some group analogues of the Skitovich–Darmois, Heyde and Kac–Bernstein characterization theorems for Q-independent random variables taking values in the group X.

Suggested Citation

  • Myronyuk, Margaryta, 2019. "Characterization of distributions of Q-independent random variables on locally compact Abelian groups," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 82-88.
    • Handle: RePEc:eee:stapro:v:152:y:2019:i:c:p:82-88
    DOI: 10.1016/j.spl.2019.04.010
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    References listed on IDEAS

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    1. Il’inskii, Alexander, 2018. "On notions of Q-independence and Q-identical distributiveness," Statistics & Probability Letters, Elsevier, vol. 140(C), pages 33-36.
    2. Kagan, Abram M. & Székely, Gábor J., 2016. "An analytic generalization of independence and identical distributiveness," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 244-248.
    3. B. L. S. Prakasa Rao, 2016. "Characterizations of Probability Distributions Through Linear Forms of Q-Conditional Independent Random Variables," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(2), pages 221-230, August.
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    Cited by:

    1. Margaryta Myronyuk, 2024. "An Analogue of the Klebanov Theorem for Locally Compact Abelian Groups," Journal of Theoretical Probability, Springer, vol. 37(3), pages 2646-2664, September.
    2. Myronyuk, Margaryta, 2021. "Characterization theorems for Q-independent random variables with values in a Banach space," Statistics & Probability Letters, Elsevier, vol. 168(C).

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    1. Myronyuk, Margaryta, 2021. "Characterization theorems for Q-independent random variables with values in a Banach space," Statistics & Probability Letters, Elsevier, vol. 168(C).
    2. B. L. S. Prakasa Rao, 2016. "Characterizations of Probability Distributions Through Linear Forms of Q-Conditional Independent Random Variables," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(2), pages 221-230, August.

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