 An ergodic theorem with weights and applications to random measures, homogenization and hydrodynamicsAlessandra Faggionato Stochastic Processes and their Applications, 2025, vol. 180, issue C Abstract: We prove a multidimensional ergodic theorem with weighted averages for the action of the group Zd on a probability space. At level n weights are of the form n−dψ(j/n), j∈Zd, for real functions ψ decaying suitably fast. We discuss applications to random measures and to quenched stochastic homogenization of random walks on simple point processes with long-range random jump rates, allowing to remove the technical Assumption (A9) from [Faggionato 2023, Theorem 4.4]. This last result concerns also some semigroup and resolvent convergence particularly relevant for the derivation of the quenched hydrodynamic limit of interacting particle systems via homogenization and duality. As a consequence we show that also the quenched hydrodynamic limit of the symmetric simple exclusion process on point processes stated in [Faggionato 2022, Theorem 4.1] remains valid when removing the above mentioned Assumption (A9). Date: 2025 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:180:y:2025:i:c:s0304414924002308 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2024.104522 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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