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Homogenization of Fractional Kinetic Equations with Random Initial Data

   
@article{EJP896,
	author = {Gi-Ren Liu and Narn-Rueih Shieh},
	title = {Homogenization of Fractional Kinetic Equations with Random Initial Data},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {16},
	year = {2011},
	keywords = {Homogenization; Small-scale limits; Riesz-Bessel fractional equation and system; Random initial data; Hermite expansion; Multiple It^\{o\}-Wiener integral; Long-range dependence},
	abstract = {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.},
	pages = {no. 32, 962-980},
	issn = {1083-6489},
	doi = {10.1214/EJP.v16-896},    
        url = {http://ejp.ejpecp.org/article/view/896}}