A stationary process is a stochastic process whose statistical properties, such as mean and variance, do not change over time. This means that the joint probability distribution of any set of observations is invariant to shifts in time, making it crucial in both theoretical and applied contexts, particularly in analyzing long-term behavior and predicting future states. The concept ties closely to ergodic theory and measure-preserving transformations, as these frameworks often assume or explore the implications of stationarity.
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