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Estimates on the tail probabilities of subordinators and applications to general time fractional equations

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  • Cho, Soobin
  • Kim, Panki

Abstract

In this paper, we study estimates on tail probabilities of several classes of subordinators under mild assumptions on the tails of their Lévy measures. As an application of that result, we obtain two-sided estimates for fundamental solutions of general homogeneous time fractional equations including those with Dirichlet boundary conditions.

Suggested Citation

  • Cho, Soobin & Kim, Panki, 2020. "Estimates on the tail probabilities of subordinators and applications to general time fractional equations," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4392-4443.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:7:p:4392-4443
    DOI: 10.1016/j.spa.2020.01.002
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    References listed on IDEAS

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    1. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1157-1160, December.
    2. Chen, Zhen-Qing, 2017. "Time fractional equations and probabilistic representation," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 168-174.
    3. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
    4. Bogdan, Krzysztof & Grzywny, Tomasz & Ryznar, Michał, 2014. "Dirichlet heat kernel for unimodal Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3612-3650.
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    Cited by:

    1. Cho, Soobin & Kim, Panki, 2021. "Estimates on transition densities of subordinators with jumping density decaying in mixed polynomial orders," Stochastic Processes and their Applications, Elsevier, vol. 139(C), pages 229-279.
    2. Hayashi, Masafumi & Takeuchi, Atsushi & Yamazato, Makoto, 2024. "Space-time boundedness and asymptotic behaviors of the densities of CME-subordinators," Stochastic Processes and their Applications, Elsevier, vol. 167(C).

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