independent increment

A stochastic processMathworldPlanetmath {X(t)tT} of real-valued random variablesMathworldPlanetmath X(t), where T is linearly orderedPlanetmathPlanetmath, is said have independent increments if for any a,b,c,dT such that a<b<c<d, X(a)-X(b) and X(c)-X(d) are independentPlanetmathPlanetmath random variables.

Remark. In case when X(t) is monotonically non-decreasing, as in the case of a counting processMathworldPlanetmath, 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