Lipschitz conditions for stochastic processes in the Banach spaces 𝔽_{𝜓}(Ω) of random variables

Zatula, D.; Kozachenko, Yu.

doi:10.1090/tpms/965

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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