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2011 Homogenization of Fractional Kinetic Equations with Random Initial Data
Gi-Ren Liu, Narn-Rueih Shieh
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Electron. J. Probab. 16: 962-980 (2011). DOI: 10.1214/EJP.v16-896


We present the small-scale limits for the homogenization of a class of spatial-temporal random fields; the field arises from the solution of a certain fractional kinetic equation and also from that of a related two-equation system, subject to given random initial data. The space-fractional derivative of the equation is characterized by the composition of the inverses of the Riesz potential and the Bessel potential. We discuss the small-scale (the micro) limits, opposite to the well-studied large-scale limits, of such spatial-temporal random field. Our scaling schemes involve both the Riesz and the Bessel parameters, and also involve the rescaling in the initial data; our results are completely new-type scaling limits for such random fields.


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Gi-Ren Liu. Narn-Rueih Shieh. "Homogenization of Fractional Kinetic Equations with Random Initial Data." Electron. J. Probab. 16 962 - 980, 2011.


Accepted: 14 April 2011; Published: 2011
First available in Project Euclid: 1 June 2016

zbMATH: 1231.60046
MathSciNet: MR2801457
Digital Object Identifier: 10.1214/EJP.v16-896

Primary: 60G60
Secondary: 60H05, 62M15


Vol.16 • 2011
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