Difference between revisions of "Stochastic boundedness"
From Encyclopedia of Mathematics
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''boundedness in probability'' | ''boundedness in probability'' | ||
| − | The property of a [[ | + | 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 $t \in \mathcal{T}$, |
| − | + | $$ | |
| − | + | \mathbf{P}\{ |X(t)| > C \} < \epsilon \ . | |
| + | $$ | ||
Latest revision as of 14:48, 21 December 2014
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=15380
Stochastic boundedness. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Stochastic_boundedness&oldid=15380
This article was adapted from an original article by A.V. Prokhorov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article