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Homestationary increment

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# 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*.

Defines:

stationary independent increment

Type of Math Object:

Definition

Major Section:

Reference

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## Mathematics Subject Classification

60G51*no label found*

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