We consider the class of simple Brown-Resnick max-stable processes whose spectral processes are continuous exponential martingales. We develop the asymptotic theory for the realized power variations of these max-stable processes, that is, sums of powers of absolute increments. We consider an infill asymptotic setting, where the sampling frequency converges to zero while the time span remains fixed. More specifically we obtain a biased central limit theorem whose bias depends on the local times of the differences between the logarithms of the underlying spectral processes.

中文翻译：

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一类Brown-Resnick过程的功率变化

我们考虑一类简单的Brown-Resnick最大稳定过程，其光谱过程是连续的指数mar。我们针对这些最大稳定过程的已实现功率变化（即绝对增量的幂之和）开发了渐近理论。我们考虑填充渐近设置，其中采样频率收敛到零，而时间跨度保持固定。更具体地说，我们获得一个有偏心的中心极限定理，其偏心取决于基础频谱过程对数之间差异的局部时间。