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Estimates on transition densities of subordinators with jumping density decaying in mixed polynomial orders

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  • Cho, Soobin
  • Kim, Panki

Abstract

In this paper, we discuss estimates on the transition densities of subordinators, which are global in time. We establish sharp two-sided estimates on the transition densities of subordinators whose Lévy measures are absolutely continuous and decaying in mixed polynomial orders. Under a weaker assumption on Lévy measures, we also obtain precise asymptotic behaviors of the transition densities at infinity. Our results cover geometric stable subordinators, Gamma subordinators and much more.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:139:y:2021:i:c:p:229-279
    DOI: 10.1016/j.spa.2021.05.005
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    References listed on IDEAS

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    1. 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.
    2. Chen, Zhen-Qing & Kumagai, Takashi, 2003. "Heat kernel estimates for stable-like processes on d-sets," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 27-62, November.
    3. 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.
    4. R. Pillai, 1990. "On Mittag-Leffler functions and related distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(1), pages 157-161, March.
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