Rough path properties for local time of symmetric α stable process

Qingfeng Wang () and Huaizhong Zhao

Stochastic Processes and their Applications, 2017, vol. 127, issue 11, 3596-3642

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 When q≥23−α, Young’s integration theory is no longer applicable.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.

Keywords: Young integral; Rough path; Local time; p-variation; α-stable processes; Itô’s formula (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.spa.2017.03.006

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