Abstract
There are obtained conditions for the convergence and estimates of the rate of convergence in terms of norms of Orlicz spaces of random series of the form
where fk(¯t) is an orthonormal system of eigenfunctions of a certain integral equation, Ξk are random variables in an Orlicz space, ¯t ε Rn.
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Literature cited
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I. N. Zelepugina and V. V. Ryazantseva, “On the rate of convergence of certain sub-Gaussian random series in norms of Orlicz spaces,” Teor. Veroyatn. Mat. Statistika,40, 28–36 (1989).
M. A. Krasnosel'skii and Ya. V. Rutitskii, Convex Functions and Orlicz Spaces [in Russian], Fizmatgiz, Moscow (1958).
Yu. V. Kozachanko, “On the uniform convergence of stochastic integrals in the norm of an Orlicz space,” Teor. Veroyatn. Mat. Statistika,29, 52–64 (1984).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 6, pp. 841–848, June, 1991.
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Trigub, S.G. On the rate of convergence of certain random series in terms of norms of Orlicz spaces. Ukr Math J 43, 789–796 (1991). https://doi.org/10.1007/BF01058949
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DOI: https://doi.org/10.1007/BF01058949