On Numerical Computation of Pickands Constants
نویسندگان
چکیده
منابع مشابه
Generalized Pickands Constants
Pickands constants play an important role in the exact asymptotic of extreme values for Gaussian stochastic processes. By the generalized Pickands constant Hη we mean the limit Hη = lim T→∞ Hη(T ) T , where Hη(T ) = IE exp ( maxt∈[0,T ] (√ 2η(t)− σ2 η(t) )) and η(t) is a centered Gaussian process with stationary increments and variance function σ2 η(t). Under some mild conditions on σ2 η(t) we ...
متن کاملProbability, Networks and Algorithms Some remarks on properties of generalized Pickands constants
We study properties of generalized Pickands constants H that appear in the extreme value theory of Gaussian processes and are de ned via the limit H lim T H T T where H T IE exp maxt T p t Var t and t is a centered Gaussian process with stationary increments We give estimates of the rate of convergence of H T T to H and prove that if n t weakly converges in C to t then under some weak condition...
متن کاملRemarks on Pickands theorem
In this article we present Pickands theorem and his double sum method. We follow Piterbarg’s proof of this theorem. Since his proof relies on general lemmas we present a complete proof of Pickands theorem using Borell inequality and Slepian lemma. The original Pickands proof is rather complicated and is mixed with upcrossing probabilities for stationary Gaussian processes. We give a lower bound...
متن کاملThe computation of classical constants.
Hypergeometric representations of classical constants and efficient algorithms for their calculation are discussed. Particular attention is devoted to algorithms for computing pi.
متن کاملRecognizing Numerical Constants
The advent of inexpensive, high-performance computers and new efficient algorithms have made possible the automatic recognition of numerically computed constants. In other words, techniques now exist for determining, within certain limits, whether a computed real or complex number can be written as a simple expression involving the classical constants of mathematics. These techniques will be il...
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: Communications for Statistical Applications and Methods
سال: 2015
ISSN: 2383-4757
DOI: 10.5351/csam.2015.22.3.277