Excursions of random fields with long range dependence

• Applicant: Professor Dr. Evgeny Spodarev
• Subject Area: Mathematics
• Term: from 2017 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 390879134

In the prolongation project we would like to determine the limiting behaviour of volumes of excursion sets of non-Gaussian subordinated random fields with long-range dependence. First, we consider the case when bivariate densities of the field have a certain diagonal expansion w.r.t an orthonormal complete system of polynomials. E.g., isotropic Gamma-marginally-distributed random fields will need Laguerre polynomials here. Second, we would like to determine the limiting behaviour of level sets' volumes for SαS moving average random fields under long memory. Third, we would like to find conditions on the kernel function when a continuous infinitely divisible moving average random field has short or long-range dependence in the sense of Definition of Kulik & Spodarev (2021) which involves volumes of their level sets.

• DFG Programme: Research Grants