Abstract
In this paper we investigate the conditions under which the distribution of i.i.d. random variables{X k } ∞ k=1 is determined by the sequence of momentsa n =E|∑ n k=1 X k |p (n=1, 2,...), where positivep is fixed.
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References
von Bahr, B., and Esseen, K.-G. (1965). Inequalities forr the absolute moment of a sum of independent random variables, 1≤r≤2.Ann. Math. Statist. 36, 299–303.
Esseen, K.-G., and Janson, S. (1985). On moment conditions for normed sums of independent random variables and martingal differences.Stoch. Proc. Appl. 9, 173–185.
Kagan, A. M., Linnik, Yu. V., and Rao, C. R. (1973).Characterization Problems in Mathematical Statistics, Wiley, New York.
Kawata, T. (1972).Fourier Analysis in Probability Theory, Academic Press, New York and London.
Lukacs, E. (1970).Characteristic Functions, 2nd ed. Griffin, London.
Neupokoeva, M. (1989). On the reconstruction of distributions by the moments of the sums of independent random variables.Stability Problems for Stochastic Models, Proceedings, VNIISI, Moscow, pp. 11–17 (Russian).
Rosenthal, H. (1970). On the subspaces ofL p (p>2) spanned by sequences of independent random variables.Israel J. Math. 8, 273–303.
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Braverman, M. A characterization of probability distributions by moments of sums of independent random variables. J Theor Probab 7, 187–198 (1994). https://doi.org/10.1007/BF02213367
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DOI: https://doi.org/10.1007/BF02213367