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