Remarks on Pickands' theorem
AbstractIn this article we present the 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 the 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 for Pickands constant. Moreover, we review equivalent definitions, simulations and bounds of Pickands constant
|Journal series||Probability and Mathematical Statistics, ISSN 0208-4147, e-ISSN 2300-8113, (A 15 pkt)|
|Publication size in sheets||1|
|Keywords in English||Stationary Gaussian process, supremum of a process, Pickands constant, fractional Brownian motion|
|Publication indicators||= 6; : 2017 = 0.448; : 2017 = 0.286 (2) - 2017=0.345 (5)|
|Citation count*||31 (2020-07-01)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.