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An approximation of stochastic processes belonging to the Orlicz space in the norm of the space $ C[0,\infty)$


Authors: Yu. V. Kozachenko and O. E. Kamenshchikova
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 88 (2013).
Journal: Theor. Probability and Math. Statist. 88 (2014), 123-138
MSC (2010): Primary 60G17; Secondary 60G07
DOI: https://doi.org/10.1090/S0094-9000-2014-00923-0
Published electronically: July 24, 2014
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Abstract: Some bounds for the distributions of increments of Orlicz stochastic processes defined in the semiaxis $ [0,\infty )$ are obtained. An approximation of such processes by integer functions of exponential type that does not exceed a number $ \gamma $ is studied in the $ C[0,\infty )$ metric with a given accuracy and reliability.


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Additional Information

Yu. V. Kozachenko
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 4E, Kiev 03127, Ukraine
Email: ykoz@ukr.net

O. E. Kamenshchikova
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 4E, Kiev 03127, Ukraine
Email: kamalev@gmail.com

DOI: https://doi.org/10.1090/S0094-9000-2014-00923-0
Keywords: Orlicz processes, bounds for the increments, approximation
Received by editor(s): March 7, 2012
Published electronically: July 24, 2014
Article copyright: © Copyright 2014 American Mathematical Society