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 the sample point $\omega$, we have a function in $t$: $X_{\omega }(t):t\mapsto X(t)$. This function $X_{\omega }(t)$ of $t$ is called a sample function, or sample path of the stochastic process.

Title	sample function
Canonical name	SampleFunction
Date of creation	2013-03-22 15:21:15
Last modified on	2013-03-22 15:21:15
Owner	gel (22282)
Last modified by	gel (22282)
Numerical id	5
Author	gel (22282)
Entry type	Definition
Classification	msc 60G17
Classification	msc 60G05
Defines	sample path