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Renormalization and homogenization of fractional diffusion equations with random data
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  • Published: November 2002

Renormalization and homogenization of fractional diffusion equations with random data

  • V. V. Anh1 &
  • N. N. Leonenko2 

Probability Theory and Related Fields volume 124, pages 381–408 (2002)Cite this article

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  • 35 Citations

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Abstract.

 This paper presents a renormalization and homogenization theory for fractional-in-space or in-time diffusion equations with singular random initial conditions. The spectral representations for the solutions of these equations are provided. Gaussian and non-Gaussian limiting distributions of the renormalized solutions of these equations are then described in terms of multiple stochastic integral representations.

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Authors and Affiliations

  1. School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Q. 4001, Australia. e-mail: v.anh@fsc.qut.edu.au, , , , , , AU

    V. V. Anh

  2. School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF2 4YH, UK. e-mail: leonenkon@Cardiff.ac.uk, , , , , , GB

    N. N. Leonenko

Authors
  1. V. V. Anh
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  2. N. N. Leonenko
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Additional information

Received: 30 May 2000 / Revised version: 9 November 2001 / Published online: 10 September 2002

Mathematics Subject Classification (2000): Primary 62M40, 62M15; Secondary 60H05, 60G60

Key words or phrases: Fractional diffusion equation – Scaling laws – Renormalised solution – Long-range dependence – Non-Gaussian scenario – Mittag-Leffler function – Stable distributions – Bessel potential – Riesz potential

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Anh, V., Leonenko, N. Renormalization and homogenization of fractional diffusion equations with random data. Probab Theory Relat Fields 124, 381–408 (2002). https://doi.org/10.1007/s004400200217

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  • Issue Date: November 2002

  • DOI: https://doi.org/10.1007/s004400200217

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Keywords

  • Integral Representation
  • Diffusion Equation
  • Spectral Representation
  • Random Data
  • Fractional Diffusion
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