stationary increment

A stochastic process $\\{X(t)\\mid t\\in T\\}$ of real-valuedrandom variables $X(t)$ , where $T$ is a subset of $\\mathbb{R}$ , issaid have stationary increments if the probabilitydistribution 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 andindependent increments is said to have stationary independentincrements.

单词	StationaryIncrement
释义	stationary increment A stochastic process $\\{X(t)\\mid t\\in T\\}$ of real-valuedrandom variables $X(t)$ , where $T$ is a subset of $\\mathbb{R}$ , issaid have stationary increments if the probabilitydistribution 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 andindependent increments is said to have stationary independentincrements.
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