Homogenization of non-symmetric jump processes

Qiao Huang, Jinqiao Duan, Renming Song

Research output: Contribution to journalArticlepeer-review


We study homogenization for a class of non-symmetric pure jump Feller processes. The jump intensity involves periodic and aperiodic constituents, as well as oscillating and non-oscillating constituents. This means that the noise can come both from the underlying periodic medium and from external environments, and is allowed to have different scales. It turns out that the Feller process converges in distribution, as the scaling parameter goes to zero, to a Lévy process. As special cases of our result, some homogenization problems studied in previous works can be recovered. We also generalize the approach to the homogenization of symmetric stable-like processes with variable order. Moreover, we present some numerical experiments to demonstrate the usage of our homogenization results in the numerical approximation of first exit times.

Original languageEnglish (US)
Pages (from-to)1-33
Number of pages33
JournalAdvances in Applied Probability
Issue number1
StatePublished - Mar 5 2024


  • Feller processes
  • Keywords:
  • non-local operators
  • stable-like processes
  • weak convergence

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics


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