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Heat kernels of non-symmetric jump processes with exponentially decaying jumping kernel

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  • Kim, Panki
  • Lee, Jaehun

Abstract

In this paper we study the transition densities for a large class of non-symmetric Markov processes whose jumping kernels decay exponentially or subexponentially. We obtain their upper bounds which also decay at the same rate as their jumping kernels. When the lower bounds of jumping kernels satisfy the weak upper scaling condition at zero, we also establish lower bounds for the transition densities, which are sharp.

Suggested Citation

  • Kim, Panki & Lee, Jaehun, 2019. "Heat kernels of non-symmetric jump processes with exponentially decaying jumping kernel," Stochastic Processes and their Applications, Elsevier, vol. 129(6), pages 2130-2173.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:6:p:2130-2173
    DOI: 10.1016/j.spa.2018.07.003
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    References listed on IDEAS

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    1. Paweł Sztonyk, 2017. "Estimates of densities for Lévy processes with lower intensity of large jumps," Mathematische Nachrichten, Wiley Blackwell, vol. 290(1), pages 120-141, January.
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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. Chen, Xin & Chen, Zhen-Qing & Wang, Jian, 2020. "Heat kernel for non-local operators with variable order," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3574-3647.
    3. Yuichi Shiozawa & Jian Wang, 2021. "Martingale Nature and Laws of the Iterated Logarithm for Markov Processes of Pure-Jump Type," Journal of Theoretical Probability, Springer, vol. 34(4), pages 2005-2032, December.

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