sample function
SampleFunction
2005-06-20 19:42:04
2008-12-17 21:58:28
Definition
stochastic process
sample path
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Let $\lbrace X(t)\mid t\in T \rbrace$ be a stochastic process, where
$X(t)$ is a random variable on the probability space
$(\Omega,\mathcal{F},\textbf{P})$. 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 \emph{sample function}, or \emph{sample path} of the
stochastic process.