Ergodicity and fluctuations of a fluid particle driven by diffusions with jumps

Guodong Pang, Nikola Sandrić

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

In this paper, we study the long-time behavior of a fluid particle immersed in a turbulent fluid driven by a diffusion with jumps, that is, a Feller process associated with a non-local operator. We derive the law of large numbers and central limit theorem for the evolution process of the tracked fluid particle in the cases when the driving process: (i) has periodic coefficients, (ii) is ergodic or (iii) is a class of Lévy processes. The presented results generalize the classical and well-known results for fluid flows driven by elliptic diffusion processes.

Original languageEnglish (US)
Pages (from-to)327-362
Number of pages36
JournalCommunications in Mathematical Sciences
Volume14
Issue number2
DOIs
StatePublished - Jan 1 2016

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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