engleski

Ergodicity and Fluctuations of a Fluid Particle Driven by Diffusions with Jumps

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.

diffusion with jumps; ergodicity; Feller process; L\'evy process; semimartingale characteristics; symbol

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