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Lipschitz conditions for stochastic processes in the Banach spaces $ \mathbb{F}_\psi(\Omega)$ of random variables


Authors: D. V. Zatula and Yu. V. Kozachenko
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 91 (2014).
Journal: Theor. Probability and Math. Statist. 91 (2015), 43-60
MSC (2010): Primary 60G07; Secondary 60G17
DOI: https://doi.org/10.1090/tpms/965
Published electronically: February 3, 2016
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Abstract: The Lipschitz continuity is studied for stochastic processes

$\displaystyle X=(X(t),t\in \mathbb{T}) $

belonging to the Banach spaces $ \mathbb{F}_\psi (\Omega )$, where $ (\mathbb{T},\rho )$ is a metric space. Some bounds for the distributions of the norms of stochastic processes in the Lipschitz spaces are also obtained.

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Additional Information

D. V. Zatula
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine
Email: dm$_$zatula@mail.ru

Yu. V. Kozachenko
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine
Email: yvk@univ.kiev.ua

DOI: https://doi.org/10.1090/tpms/965
Keywords: Banach spaces $\mathbb{F}_\psi(\Omega)$, stochastic processes, Lipschitz conditions, continuity modulus, metric massiveness
Received by editor(s): June 23, 2014
Published electronically: February 3, 2016
Article copyright: © Copyright 2016 American Mathematical Society