Ergodicity and fluctuations of a fluid particle driven by diffusions with jumps
Probability
2015-02-17 v1
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 L\'evy processes. The presented results generalize the classical and well-known results for fluid flows driven by elliptic diffusion processes.
Cite
@article{arxiv.1502.04440,
title = {Ergodicity and fluctuations of a fluid particle driven by diffusions with jumps},
author = {Guodong Pang and Nikola Sandrić},
journal= {arXiv preprint arXiv:1502.04440},
year = {2015}
}