Research student’s zoom progress talk

Event status:

You are welcome to attend the following Statistics and Stochastic colloquium (part of the Colloquium Series of the Department of Mathematics and Statistics) at La Trobe University.

Friday 04 September 2020 12:00 pm (Add to calendar)
Andriy Olenko
Presented by:
Illia Donhauzer
Type of Event:

Title: On the asymptotic behaviour of functionals of random fields

Abstract: The talk is about the asymptotic behaviour of functionals of long-range dependent random fields. The Strong Law of Large Numbers (SLLN) and new properties of the limit processes in the Non-central Limit Theorem (NLT) will be discussed.

The SLLN for integral functionals of random fields with unboundedly increasing covariances will be presented. The SLLN is derived for the case of increasing domains. Conditions on covariance functions such that the SLLN holds will be provided. The considered scenarios include non-stationary random fields. The discussion about applications to weak and long-range dependent random fields and numerical examples will be shown.

New properties of generalized Hermite-type processes that arise in NLT for integral functionals of long-range dependent random fields will be demonstrated. Contrary to the classical one-dimensional case, it will be shown that for any choice of a multidimensional observation window the generalized Hermite-type process has non-stationary increments.




25th Sep 2020 5:25am

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