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Stochastic boundedness

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boundedness in probability

The property of a stochastic process $X(t)$, $t \in \mathcal{T}$, expressed by the condition: For an arbitrary $\epsilon > 0$ there exists a $C > 0$ such that for all $t \in \mathcal{T}$, $$ \mathbf{P}\{ |X(t)| > C \} < \epsilon \ . $$

How to Cite This Entry:
Stochastic boundedness. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Stochastic_boundedness&oldid=35772
This article was adapted from an original article by A.V. Prokhorov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article