Abstract
We construct an example that demonstrates that natural restrictions imposed on finite convolutions of singular distributions do not guarantee the purity of the limit distribution.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
B. Jessen and A. Wintner, “Distribution functions and the Riemann Zeta function,” Trans. Amer. Math. Soc., 38, 48–88 (1935).
E. Lukacs, Characteristic Functions, Griffin, London (1970).
V. M. Zolotarev and V. M. Kruglov, “Structure of infinitely divisible distributions on a locally compact Abel group,” Teor. Ver. Primen., 20, No. 4, 712–724 (1975).
Ya. F. Vinnishin and V. A. Moroka, “On the distribution function of a sum of independent random processes,” in: Selected Problems of Contemporary Theory of Random Processes [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1988).
Ya. F. Vinnishin, “On convolutions of singular distribution functions,” in: Stochastic Analysis and Its Applications [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1989).
Ya. F. Vinnishin and V. A. Moroka, “On convolutions of singular distribution functions and analogs of the Jessen – Wintner theorem,” in: Random Processes and Infinite-Dimensional Analysis [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1992).
M. V. Prats'ovytyi, “On finite convolutions of singular distributions and a singular analog of the Jessen – Wintner theorem,” Ukr. Mat. Zh., 50, No. 8, 1082–1088 (1998).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Vynnyshyn, Y.F. Convolutions of Singular Distribution Functions. Ukrainian Mathematical Journal 56, 148–152 (2004). https://doi.org/10.1023/B:UKMA.0000031709.03258.e4
Issue Date:
DOI: https://doi.org/10.1023/B:UKMA.0000031709.03258.e4