On Extremal Index of Max-Stable Random Fields
نویسندگان
چکیده
For a given stationary max-stable random field X(t), t ∈ ℤd, the corresponding generalized Pickands constant coincideswith classical extremal index θX [0, 1]. In this contribution,we discuss necessary and sufficient conditions for to be 0, positive, or equal 1 also show that is so-called block index. Further, we consider some general functional indices of X prove large class functionals they coincide with θX.
منابع مشابه
Extremal shot noises, heavy tails and max-stable random fields
We consider the extremal shot noise defined by M(y) = sup{mh(y − x); (x,m) ∈ Φ}, where Φ is a Poisson point process on R × (0,+∞) with intensity λdxG(dm) and h : R → [0,+∞] is a measurable function. Extremal shot noises naturally appear in extreme value theory as a model for spatial extremes and serve as basic models for annual maxima of rainfall or for coverage field in telecommunications. In ...
متن کاملHow to compute the extremal index of stationary random fields
We present local dependence conditions for stationary random fields under which the extremal index and the asymptotic distribution of the maximum M(n1,...,nd) can be calculated from the joint distribution of a finite number s1s2 of variables. keywords: Extremal index, local and long range dependence, random field.
متن کاملOn Approximating Max-stable Processes and Constructing Extremal Copula Functions
There is an infinite number of parameters in the definition of multivariate maxima of moving maxima (M4) processes, which poses challenges in statistical applications where workable models are preferred. This paper establishes sufficient conditions under which an M4 process with infinite number of parameters may be approximated by an M4 process with finite number of parameters. In statistical i...
متن کاملOn Optimal Exact Simulation of Max-stable and Related Random Fields on a Compact Set
We consider the random field M(t) = sup n≥1 { − logAn +Xn(t) } , t ∈ T , for a set T ⊂ R, where (Xn) is an iid sequence of centered Gaussian random fields on T and 0 < A1 < A2 < · · · are the arrivals of a general renewal process on (0,∞), independent of (Xn). In particular, a large class of max-stable random fields with Gumbel marginals have such a representation. Assume that one needs c (d) =...
متن کاملThe Extremal Index for a Random Tessellation
Let m be a random tessellation in R, d ≥ 1, observed in the window Wρ = ρ1/d[0, 1], ρ > 0, and let f be a geometrical characteristic. We investigate the asymptotic behaviour of the maximum of f(C) over all cells C ∈ m with nucleus in Wρ as ρ goes to infinity. When the normalized maximum converges, we show that its asymptotic distribution depends on the so-called extremal index. Two examples of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Lithuanian Mathematical Journal
سال: 2021
ISSN: ['1573-8825', '0363-1672']
DOI: https://doi.org/10.1007/s10986-021-09519-8