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stationary increment (Definition)

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.



"stationary increment" is owned by CWoo.
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Also defines:  stationary independent increment
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Cross-references: independent increments, function, fixed, probability distribution function, subset, random variables, stochastic process
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This is version 6 of stationary increment, born on 2005-02-09, modified 2005-02-28.
Object id is 6732, canonical name is StationaryIncrements.
Accessed 4140 times total.

Classification:
AMS MSC: 60G51 (Probability theory and stochastic processes :: Stochastic processes :: Processes with independent increments)
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