Семинары: W. Karcher, A central limit theorem for the volume of the excursion sets of associated stochastically continuous stationary random fields

СЕМИНАРЫ


Городской семинар по теории вероятностей и математической статистике 29 апреля 2011 г. 18:00, г. Санкт-Петербург, ПОМИ, ауд. 311 (наб. р. Фонтанки, 27)

A central limit theorem for the volume of the excursion sets of associated stochastically continuous stationary random fields W. Karcher
Аннотация: In [1], the multivariate central limit theorem (CLT) for the volumes of excursion sets of stationary quasi-associated random fields on $\mathbb R^d$ is proved. We extend their results by considering associated stochastically continuous stationary random fields which need not necessarily have second moments. Based on the CLT, we construct a statistical hypothesis test and provide simple conditions on the tail behavior of the kernel functions for certain max-stable and sum-stable random fields with spectral representation such that the assumptions of the CLT are satisfied. [1] Bulinski, A., Spodarev, E. and Timmermann, F., Central limit theorems for the excursion sets volumes of weakly dependent random fields, accepted at Bernoulli, 2010. Язык доклада: английский