Communications in Mathematical Sciences
Volume 14 (2016)
Ergodicity and fluctuations of a fluid particle driven by diffusions with jumps
Pages: 327 – 362
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.
diffusion with jumps, ergodicity, Feller process, Lévy process, semi-martingale characteristics, symbol
2010 Mathematics Subject Classification
60F17, 60G17, 60J75