In this paper, we generalize the Preisach model to the case when parameters of elementary relays are random variables. We show that an output state of the stochastic Preisach operator can be treated as a random process. For this random process the first and second statistical moments are obtained in an explicit form. We prove also the correctness of the definition of such an operator. Illustrative numerical examples are also presented and discussed.

中文翻译：

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随机Preisach运算符：设计方法中的定义

在本文中，我们将Preisach模型推广到基本继电器参数为随机变量的情况。我们证明了随机Preisach算子的输出状态可以看作是一个随机过程。对于该随机过程，以显式形式获得第一和第二统计矩。我们还证明了这种运算符定义的正确性。还提供了示例性的数值示例并进行了讨论。