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Rough path properties for local time of symmetric α stable process

Author

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  • Wang, Qingfeng
  • Zhao, Huaizhong

Abstract

In this paper, we first prove that the local time associated with symmetric α-stable processes is of bounded p-variation for any p>2α−1 partly based on Barlow’s estimation of the modulus of the local time of such processes.The fact that the local time is of bounded p-variation for any p>2α−1 enables us to define the integral of the local time ∫−∞∞▿−α−1f(x)dxLtx as a Young integral for less smooth functions being of bounded q-variation with 1≤q<23−α. When q≥23−α, Young’s integration theory is no longer applicable. However, rough path theory is useful in this case. The main purpose of this paper is to establish a rough path theory for the integration with respect to the local times of symmetric α-stable processes for 23−α≤q<4.

Suggested Citation

  • Wang, Qingfeng & Zhao, Huaizhong, 2017. "Rough path properties for local time of symmetric α stable process," Stochastic Processes and their Applications, Elsevier, vol. 127(11), pages 3596-3642.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:11:p:3596-3642
    DOI: 10.1016/j.spa.2017.03.006
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