A stochastic process $\lbrace X(t)\mid t\in T\rbrace$ 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.