sample function

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