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Space-time boundedness and asymptotic behaviors of the densities of CME-subordinators

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  • Hayashi, Masafumi
  • Takeuchi, Atsushi
  • Yamazato, Makoto

Abstract

In this article, we consider subordinators whose Lévy measures are represented as Laplace transforms of measures on (0,∞). We shall call them CME-subordinators. Transition probabilities of such processes without drifts are absolutely continuous on (0,∞) with respect to Lebesgue measure on (0,∞). We show that the densities are space–time bounded on [t1,∞)×[x1,∞) for each t1>0 and x1>0, and the supremum of the densities with respect to space variable tends to zero as time goes to infinity. Moreover, we point out that the speed of decrease is closely related to the behavior near the origin of the corresponding Lévy density.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:spapps:v:167:y:2024:i:c:s0304414923002041
    DOI: 10.1016/j.spa.2023.104232
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    References listed on IDEAS

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    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. 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.
    3. Makoto Yamazato, 2006. "Topics Related to Gamma Processes," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 5, pages 157-182, World Scientific Publishing Co. Pte. Ltd..
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    2. 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.

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