【摘 要】
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Stationarity is the shift invariance of the distribution for a stochastic process. In this work we rediscover stationarity as a path property rather than a
【出 处】
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2015 Peking University Youth Probability Forum(2015年北京大学青年概率
论文部分内容阅读
Stationarity is the shift invariance of the distribution for a stochastic process. In this work we rediscover stationarity as a path property rather than a distributional property. More precisely, we characterize a set of paths denoted as A, which corresponds to the notion of stationarity in the following sense: on one hand, the set A is shown to be large enough, so that for any stationary process, almost all of its paths are in A; on the other hand, we prove that any path in A will behave in the optimal way under any stationarity test satisfying some mild conditions. The results justify our intuition about how a typical stationary process should look like, and potentially lead to new families of stationarity tests.
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