Literature cited
N. A. Sapogov, “Stability for the Marcinkiewicz theorem. The case of a quartic polynomial,”Zap. Nauch. Sem. LOMI,61, 107–124 (1976).
N. A. Sapogov, “The problem of stability for the Marcinkiewicz theorem,”Zap. Nauch. Sem. LOMI,87, 104–124 (1979).
A. A. Zinger and R. V. Yanushkyavichyus, “On a theorem of characterization by identical statistical distributions and its stability,”Probl. Ustoich. Stokh. Mod.: Trudy Sem., VNIISI, Moscow, 32–46 (1980).
A. A. Zinger and R. V. Yanushkyavichyus, “Stability of a characterization theorem of Yu. V. Linnik,”Probl. Ustoich. Stokh. Mod.: Trudy Sem., VNIISI, Moscow, 24–30 (1980).
Yu. V. Linnik and I. V. Ostrovskii,Decompositions of Random Variables and Vectors, American Mathematical Society, Providence (1977).
N. A. Sapogov, “The stability problem in the uniqueness theorem for a characteristic function that is analytic in a neighborhood of the origint=0,”Probl. Ustoich. Stokh. Mod.: Trudy Sem., VNIISI, Moscow, 88–94 (1980).
A. O. Gel'fond,The Calculus of Finite Differences [Russian], Nauka, Moscow (1967).
A. I. Markushevich,Theory of Functions of a Complex Variable, Vol. 2, Prentice-Hall, Englewood Cliffs, NJ (1966). Vol. 2, Nauka, Moscow (1968).
A. M. Kaga.n, Yu. V. Linnik, and S. R. Rao,Characterization Problems in Mathematical Statistics Wiley, New York (1973).
G. P. Chistyakov, “On the accuracy of estimates in theorems on the stability of expansions of the normal and Poisson distributions,”Teor. Funkts., Funktsional. Anal. i Pril., No. 26, 119–128 (1975).
L. B. Golinskii, “On an estimate of the stability in the Marcinkiewicz theorem for quartic polynomials,” in:Mathematical Physics and Functional Analysis [Russian], Naukova Dumka, Kiev (1986), pp. 118–126.
G. Polya, G. Szegö,Problems and Theorems in Analysis, Vol. 1, Springer, New York (1972).
Additional information
Translated fromProblemy Ustoichivosti Stokhasticheskikh Modelei, Trudy Seminara, pp. 8–24, 1988.
The author is deeply grateful to G. P. Chistyakov for constant attention to this work and helpful comments.
Rights and permissions
About this article
Cite this article
Golinskii, L.B. Stability estimates in the theorem of J. Marcinkiewicz. J Math Sci 57, 3193–3209 (1991). https://doi.org/10.1007/BF01099017
Issue Date:
DOI: https://doi.org/10.1007/BF01099017