High-Level Moving Excursions for Spatiotemporal Gaussian Random Fields with Long Range Dependence Leonenko, Nikolai Ruiz Medina, María Dolores Central limit theorem Gaussian subordinated random fields LRD in physics Moving levels Reduction theorems The first author was partially supported by the Croatian Science Foundation (HRZZ) grant Scaling in Stochastic Models (IP-2022-10-8081). He also was supported in part by ARC Discovery Grant DP220101680 (Australia), LMS grant 42997 (UK) and grant FAPESP 22/09201-8 (Brazil). The second author was supported in part by MCIN/ AEI/PID2022-142900NB-I00, and CEX2020-001105-M MCIN/ AEI/10.13039/501100011033). The asymptotic behavior of an extended family of integral geometric random functionals, including spatiotemporal Minkowski functionals under moving levels, is analyzed in this paper. Specifically, sojourn measures of spatiotemporal long-range dependence (LRD) Gaussian random fields are considered in this analysis. The limit results derived provide general reduction principles under increasing domain asymptotics in space and time. The case of time-varying thresholds is also studied. Thus, the family of morphological measures considered allows the statistical and geometrical analysis of random physical systems displaying structural changes over time. Motivated by cosmological applications, the derived results are applied to the context of sojourn measures of spatiotemporal spherical Gaussian random fields. The results are illustrated for some families of spatiotemporal Gaussian random fields displaying complex spatiotemporal dependence structures. 2025-03-04T11:32:42Z 2025-03-04T11:32:42Z 2025-01-16 journal article Leonenko, N., Ruiz-Medina, M.D. High-Level Moving Excursions for Spatiotemporal Gaussian Random Fields with Long Range Dependence. J Stat Phys 192, 19 (2025). https://doi.org/10.1007/s10955-025-03396-y https://hdl.handle.net/10481/102841 10.1007/s10955-025-03396-y eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional Springer Nature