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Time fractional equations and probabilistic representation

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  • Chen, Zhen-Qing

Abstract

In this paper, we study the existence and uniqueness of solutions for general fractional-time parabolic equations of mixture type, and their probabilistic representations in terms of the corresponding inverse subordinators with or without drifts. An explicit relation between occupation measure for Markov processes time-changed by inverse subordinator in open sets and that of the original Markov process in the open set is also given.

Suggested Citation

  • Chen, Zhen-Qing, 2017. "Time fractional equations and probabilistic representation," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 168-174.
    • Handle: RePEc:eee:chsofr:v:102:y:2017:i:c:p:168-174
    DOI: 10.1016/j.chaos.2017.04.029
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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. Meerschaert, Mark M. & Scheffler, Hans-Peter, 2008. "Triangular array limits for continuous time random walks," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1606-1633, September.
    3. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
    4. Meerschaert, Mark M. & Scheffler, Hans-Peter, 2006. "Stochastic model for ultraslow diffusion," Stochastic Processes and their Applications, Elsevier, vol. 116(9), pages 1215-1235, September.
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    Cited by:

    1. 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.
    2. D’Ovidio, Mirko & Loreti, Paola, 2018. "Solutions of fractional logistic equations by Euler’s numbers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 1081-1092.
    3. Mirko D’Ovidio, 2022. "On the Non-Local Boundary Value Problem from the Probabilistic Viewpoint," Mathematics, MDPI, vol. 10(21), pages 1-26, November.
    4. Zhang, Shuaiqi & Chen, Zhen-Qing, 2022. "Fokker–Planck equation for Feynman–Kac transform of anomalous processes," Stochastic Processes and their Applications, Elsevier, vol. 147(C), pages 300-326.
    5. D’Ovidio, Mirko & Iafrate, Francesco, 2024. "Elastic drifted Brownian motions and non-local boundary conditions," Stochastic Processes and their Applications, Elsevier, vol. 167(C).
    6. Du, Qiang & Toniazzi, Lorenzo & Zhou, Zhi, 2020. "Stochastic representation of solution to nonlocal-in-time diffusion," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 2058-2085.

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