Electronic Journal of Probability

Diffusion in Long-Range Correlated Ornstein-Uhlenbeck Flows

Albert Fannjiang and Tomasz Komorowski

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Abstract

We study a diffusion process with a molecular diffusion and random Markovian-Gaussian drift for which the usual (spatial) Peclet number is infinite. We introduce a temporal Peclet number and we prove that, under the finiteness of the temporal Peclet number, the laws of diffusions under the diffusive rescaling converge weakly, to the law of a Brownian motion. We also show that the effective diffusivity has a finite, nonzero limit as the molecular diffusion tends to zero.

Article information

Source
Electron. J. Probab., Volume 7 (2002), paper no. 20, 22 pp.

Dates
Accepted: 31 May 2002
First available in Project Euclid: 16 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1463434893

Digital Object Identifier
doi:10.1214/EJP.v7-119

Mathematical Reviews number (MathSciNet)
MR1943893

Zentralblatt MATH identifier
1007.60017

Subjects
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 35B27: Homogenization; equations in media with periodic structure [See also 74Qxx, 76M50]

Keywords
Ornstein-Uhlenbeck flow martingale central limit theorem homogenization Peclet number

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Fannjiang, Albert; Komorowski, Tomasz. Diffusion in Long-Range Correlated Ornstein-Uhlenbeck Flows. Electron. J. Probab. 7 (2002), paper no. 20, 22 pp. doi:10.1214/EJP.v7-119. https://projecteuclid.org/euclid.ejp/1463434893


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