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Scaling laws for fractional diffusion-wave equations with singular data

Author

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  • Anh, V. V.
  • Leonenko, N. N.

Abstract

Gaussian and non-Gaussian limiting distributions of the rescaled solutions of the fractional (in time) diffusion-wave equation for Gaussian and non-Gaussian initial data with long-range dependence are described in terms of multiple Wiener-Itô integrals.

Suggested Citation

  • Anh, V. V. & Leonenko, N. N., 2000. "Scaling laws for fractional diffusion-wave equations with singular data," Statistics & Probability Letters, Elsevier, vol. 48(3), pages 239-252, July.
    • Handle: RePEc:eee:stapro:v:48:y:2000:i:3:p:239-252
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    References listed on IDEAS

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    1. Anh, V. V. & Leonenko, N. N., 1999. "Non-Gaussian scenarios for the heat equation with singular initial conditions," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 91-114, November.
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    Cited by:

    1. Rui, Weiguo, 2018. "Idea of invariant subspace combined with elementary integral method for investigating exact solutions of time-fractional NPDEs," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 158-171.
    2. Deng, Kaiying & Chen, Minghua & Sun, Tieli, 2015. "A weighted numerical algorithm for two and three dimensional two-sided space fractional wave equations," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 264-273.
    3. Abel Garcia-Bernabé & S. I. Hernández & L. F. Del Castillo & David Jou, 2016. "Continued-Fraction Expansion of Transport Coefficients with Fractional Calculus," Mathematics, MDPI, vol. 4(4), pages 1-10, December.
    4. Jumarie, Guy, 2009. "From Lagrangian mechanics fractal in space to space fractal Schrödinger’s equation via fractional Taylor’s series," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1590-1604.
    5. Das, S., 2009. "A note on fractional diffusion equations," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2074-2079.
    6. Jumarie, Guy, 2007. "Lagrangian mechanics of fractional order, Hamilton–Jacobi fractional PDE and Taylor’s series of nondifferentiable functions," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 969-987.
    7. O. E. Barndorff-Nielsen & N. N. Leonenko, 2005. "Spectral Properties of Uperpositions of Ornstein-Uhlenbeck Type Processes," Methodology and Computing in Applied Probability, Springer, vol. 7(3), pages 335-352, September.

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