# independent increment

A stochastic process^{} $\{X(t)\mid t\in T\}$ of real-valued
random variables^{} $X(t)$, where $T$ is linearly ordered^{}, is said have
*independent increments* if for any $a,b,c,d\in T$ such that $$, $X(a)-X(b)$ and $X(c)-X(d)$ are independent^{} random
variables.

Remark. In case when $X(t)$ is monotonically non-decreasing,
as in the case of a counting process^{}, it is customary to write
$X(b)-X(a)$ and $X(d)-X(c)$ instead of the above to emphasize the
comparison of two positive quantities (for example, the numbers of
occurrences of a certain event in some time intervals).

Title | independent increment |
---|---|

Canonical name | IndependentIncrement |

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

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

Owner | CWoo (3771) |

Last modified by | CWoo (3771) |

Numerical id | 4 |

Author | CWoo (3771) |

Entry type | Definition |

Classification | msc 60G51 |