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

2015/02/16 by Guodong Pang, Nikola Sandrić, Pang, Guodong +1
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · Mathematics · #60F17 #60G17 #60J75 #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1502.04440

openalex publication_date 2015/02/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• Symmetric Stable Laws and Stable-Like Jump-Diffusions

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