# stationary increment

A stochastic process^{} $\{X(t)\mid t\in T\}$ of real-valued
random variables^{} $X(t)$, where $T$ is a subset of $\mathbb{R}$, is
said have *stationary increments* if the probability
distribution function for $X(s+t)-X(s)$ is fixed (the same) for all
$s\in T$ such that $s+t\in T$. In other words, the distribution for $X(s+t)-X(s)$ is a function of “how long” or $t$, not “when” or $s$.

A stochastic process that possesses both stationary increments and
independent increments is said to have *stationary independent
increments*.

Title | stationary increment |
---|---|

Canonical name | StationaryIncrement |

Date of creation | 2013-03-22 15:01:25 |

Last modified on | 2013-03-22 15:01:25 |

Owner | CWoo (3771) |

Last modified by | CWoo (3771) |

Numerical id | 9 |

Author | CWoo (3771) |

Entry type | Definition |

Classification | msc 60G51 |

Defines | stationary independent increment |