# 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 StationaryIncrement 2013-03-22 15:01:25 2013-03-22 15:01:25 CWoo (3771) CWoo (3771) 9 CWoo (3771) Definition msc 60G51 stationary independent increment