具有独立切换时间的非对称切换过程的特征
Characteristics of asymmetric switch processes with independent switching times
AI总结：
本文研究具有独立切换时间的非对称切换过程的非平稳与平稳版本的特征，证明了期望值函数单调性与服从几何项数的随机和形式区间分布的等价性，并推导了特征对应有效区间分布的条件。
摘要：
非对称切换过程是一种在取值1和-1之间交替的二元随机过程，其处于这些状态的时间分布可能不同。本文考虑了该过程的两种版本：一种是在零时刻以一次切换启动的非平稳版本，另一种是由非平稳版本构造的平稳版本。研究了这两种过程的特征，例如期望值和协方差。主要结果表明，期望值函数的单调性与区间分布之间存在等价关系，该区间分布具有以随机变量之和形式呈现的随机表示，其中项数服从几何分布。这种表示可以自然解释为切换尝试可能随机失败的模型。基于这些结果，本文推导了这些特征能导出有效区间分布的条件，这在应用中至关重要。
英文摘要：
The asymmetric switch process is a binary stochastic process that alternates between the values one and minus one, where the distributions of the time in these states may differ. Two versions of the process are considered: a non-stationary version that starts with a switch at time zero and a stationary one constructed from the non-stationary one. Characteristics of these two processes, such as the expected values and covariance, are investigated. The main results show an equivalence between the monotonicity of the expected value functions and the distribution of the intervals having a stochastic representation in the form of a sum of random variables, where the number of terms follows a geometric distribution. This representation has a natural interpretation as a model in which switching attempts may fail at random. From these results, conditions are derived when these characteristics lead to valid interval distributions, which is vital in applications.
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