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Distribution of the supremum of random processes from quasi-BanachK σ-spaces

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Abstract

We study random processes from quasi-BanachK σ-spaces of random variables whose domain of definition is not necessarily a compact set. We establish conditions under which the supremum of a properly normalized process belongs to the same space as the process itself. We also obtain estimates for the norm of this supremum.

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Authors
  1. Yu. V. Kozachenko
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Additional information

Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 7, pp. 918–930, July, 1999.

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Kozachenko, Y.V. Distribution of the supremum of random processes from quasi-BanachK σ-spaces. Ukr Math J 51, 1029–1043 (1999). https://doi.org/10.1007/BF02592039

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  • DOI: https://doi.org/10.1007/BF02592039

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