stationary increment

A stochastic process $\{X(t)\mid t\in T\}$ of real-valued random variables $X(t)$, where $T$ is a subset of $ℝ$, 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