# sample function

Let $\{X(t)\mid t\in T\}$ be a stochastic process^{}, where
$X(t)$ is a random variable^{} on the probability space^{}
$(\mathrm{\Omega},\mathcal{F},\text{\mathbf{P}})$. 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 |