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Singularly perturbed telegraph equations with applications in the random walk theory

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  • Jacek Banasiak
  • Janusz R. Mika

Abstract

In the paper we analyze singularly perturbed telegraph systems applying the newly developed compressed asymptotic method and show that the diffusion equation is an asymptotic limit of singularly perturbed telegraph system of equations. The results are applied to the random walk theory for which the relationship between correlated and uncorrelated random walks is explained in asymptotic terms.

Suggested Citation

  • Jacek Banasiak & Janusz R. Mika, 1998. "Singularly perturbed telegraph equations with applications in the random walk theory," International Journal of Stochastic Analysis, Hindawi, vol. 11, pages 1-20, January.
    • Handle: RePEc:hin:jnijsa:564729
    DOI: 10.1155/S1048953398000021
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    Cited by:

    1. Weam Alharbi & Sergei Petrovskii, 2018. "Critical Domain Problem for the Reaction–Telegraph Equation Model of Population Dynamics," Mathematics, MDPI, vol. 6(4), pages 1-15, April.
    2. M. Consuelo Casabán & Rafael Company & Lucas Jódar, 2019. "Numerical Integral Transform Methods for Random Hyperbolic Models with a Finite Degree of Randomness," Mathematics, MDPI, vol. 7(9), pages 1-21, September.
    3. Hosseininia, M. & Heydari, M.H., 2019. "Meshfree moving least squares method for nonlinear variable-order time fractional 2D telegraph equation involving Mittag–Leffler non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 389-399.
    4. Vieira, N. & Ferreira, M. & Rodrigues, M.M., 2022. "Time-fractional telegraph equation with ψ-Hilfer derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

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