# sample function

Let $\{X(t)\mid t\in T\}$ 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 sample function, or sample path of the stochastic process.

Title sample function SampleFunction 2013-03-22 15:21:15 2013-03-22 15:21:15 gel (22282) gel (22282) 5 gel (22282) Definition msc 60G17 msc 60G05 sample path