Abstract
We present a general framework for weak convergence to decorated Lévy processes in enriched spaces of càdlàg functions for vector-valued processes arising in deterministic systems. Applications include uniformly expanding maps and unbounded observables as well as nonuniformly expanding/hyperbolic maps with bounded observables. The latter includes intermittent maps and dispersing billiards with flat cusps. In many of these examples, convergence fails in all of the Skorohod topologies. Moreover, the enriched space picks up details of excursions that are not recorded by Skorohod or Whitt topologies.
Funding Statement
ACMF, JMF and MT were partially supported by FCT projects PTDC/MAT-PUR/4048/2021 and 2022.07167.PTDC, with national funds, and by CMUP, which is financed by national funds through FCT – Fundação para a Ciência e a Tecnologia, I.P., under the project with reference UIDB/00144/2020.
Acknowledgments
IM and MT are grateful to hospitality at the University of Porto where part of this work was done.
Citation
Ana Cristina Moreira Freitas. Jorge Milhazes Freitas. Ian Melbourne. Mike Todd. "Convergence to decorated Lévy processes in non-Skorohod topologies for dynamical systems." Electron. J. Probab. 29 1 - 24, 2024. https://doi.org/10.1214/24-EJP1231
Information
