Homogenization of fractional kinetic equations with random initial data

Gi-Ren Liu, Narn Rueih Shieh

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)962-980
Number of pages19
JournalElectronic Journal of Probability
Volume16
DOIs
Publication statusPublished - 2011 Jan 1

Fingerprint

Kinetic Equation
Homogenization
Random Field
Fractional
Bessel Potential
Riesz Potential
Scaling Limit
Rescaling
Friedrich Wilhelm Bessel
Fractional Derivative
Scaling
Kinetics
Random field

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

@article{95bda6982bb047a5858819e5d4fc7ac4,
title = "Homogenization of fractional kinetic equations with random initial data",
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.",
author = "Gi-Ren Liu and Shieh, {Narn Rueih}",
year = "2011",
month = "1",
day = "1",
doi = "10.1214/EJP.v16-896",
language = "English",
volume = "16",
pages = "962--980",
journal = "Electronic Journal of Probability",
issn = "1083-6489",
publisher = "Institute of Mathematical Statistics",

}

Homogenization of fractional kinetic equations with random initial data. / Liu, Gi-Ren; Shieh, Narn Rueih.

In: Electronic Journal of Probability, Vol. 16, 01.01.2011, p. 962-980.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Homogenization of fractional kinetic equations with random initial data

AU - Liu, Gi-Ren

AU - Shieh, Narn Rueih

PY - 2011/1/1

Y1 - 2011/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79957469482&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79957469482&partnerID=8YFLogxK

U2 - 10.1214/EJP.v16-896

DO - 10.1214/EJP.v16-896

M3 - Article

VL - 16

SP - 962

EP - 980

JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

SN - 1083-6489

ER -