Finite-Dimensional Distributions and Tail Behavior in Stationary Interval-Valued Probability Models
平稳区间值概率模型的有限维分布与尾部行为
We consider the relationship between the finite-dimensional distributions of a stationary time series model and its asymptotic behavior in the framework of interval-valued probability (IVP), a simple generalization of additive probability measures. By Caratheodory's theorem, the specification of a countably additive probability measure on the algebra of cylinders $\mathscr{C}$ uniquely defines its behavior on $\sigma(\mathscr{C})$ (containing the tail events). If the measure…