论文标题
开关过程的特征和几何分裂性
Characteristics of the switch process and geometric divisibility
论文作者
论文摘要
开关过程在1和-1之间独立交替，第一个开关在原点处出现1。此过程的预期价值函数是通过切换时间的分布来唯一定义的。两者之间的关系是通过拉普拉斯变换隐式描述的，这很难确定给定函数是否是某些开关过程的预期值函数。在预期值函数的单调性的假设下，我们得出了明确的关系。结果表明，几何可划分的切换时间分布对应于非负值降低的期望值函数。此外，可以获得开关过程静止对应物的开关时间分布与自动增强功能之间的显式关系，这允许固定开关过程及其协方差函数并行结果。这些结果适用于统计物理学中的近似方法，并提供了一个示例。
The switch process alternates independently between 1 and -1, with the first switch to 1 occurring at the origin. The expected value function of this process is defined uniquely by the distribution of switching times. The relation between the two is implicitly described through the Laplace transform, which is difficult to use for determining if a given function is the expected value function of some switch process. We derive an explicit relation under the assumption of monotonicity of the expected value function. It is shown that geometric divisible switching time distributions correspond to a non-negative decreasing expected value function. Moreover, an explicit relation between the switching time distribution and the autocovariance function of the switch process stationary counterpart is obtained, which allows parallel results for the stationary switch process and its covariance function. These results are applicable to approximation methods in statistical physics, and an example is presented.
