In this paper, we consider isotropic and stationary max-stable, inverse max-stable and max-mixture processes $X=(X(s){)}_{s\in {\mathbb{R}}^2}$ and the damage process ${\mathcal{D}}_X^{\nu }=|X{|}^{\nu }$ with $0<\nu <1/2$. We study the quantitative behaviour of a risk measure which is the variance of the average of ${\mathcal{D}}_X^{\nu }$ over a region $\mathcal{A}\subset {\mathbb{R}}^2$. This kind of risk measure has already been introduced and studied for some max-stable processes in Koch [Spatial risk measures and applications to max-stable processes, Extremes 20(3) (2017), pp. 635–670].

在本文中，我们考虑了各向同性和平稳的最大稳态，逆最大稳态和最大混合过程 $X=（X（s）{）}_{s\in {\mathbb{[R}}^2}$ 和破坏过程 ${\mathcal{d}}_X^{\nu }=|X{|}^{\nu }$ 与 $0<\nu <\mathrm{1个}/2$。我们研究了风险度量的量化行为，即风险平均值的方差${\mathcal{d}}_X^{\nu }$ 在一个地区 $\mathcal{一种}\subset {\mathbb{[R}}^2$。在Koch中，已经针对某些最大稳定过程引入并研究了这种风险度量[空间风险度量及其在最大稳定过程中的应用，极端20（3）（2017），第635-670页]。