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[parent] sample function (Definition)

Let $\lbrace X(t)\mid t\in T \rbrace$ be a stochastic process, where $X(t)$ is a random variable on the probability space $(\Omega,\mathcal{F},{P})$ Writing $X(t)$ as $X(t,\omega)$ where $t\in T$ and $\omega\in\Omega$ we see that if we fix the sample point $\omega$ we have a function in $t$ $X_{\omega}(t) \colon t\mapsto X(t)$ This function $X_{\omega}(t)$ of $t$ is called a sample function, or sample path of the stochastic process.




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Also defines:  sample path

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Cross-references: function, point, fix, probability space, random variable, stochastic process
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This is version 2 of sample function, born on 2005-06-20, modified 2008-12-17.
Object id is 7176, canonical name is SampleFunction.
Accessed 2926 times total.

Classification:
AMS MSC60G05 (Probability theory and stochastic processes :: Stochastic processes :: Foundations of stochastic processes)
 60G17 (Probability theory and stochastic processes :: Stochastic processes :: Sample path properties)

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