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Harnack inequalities for Ornstein-Uhlenbeck processes driven by Lévy processes

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  • Wang, Jian

Abstract

By using the existing sharp estimates of the density function for rotationally invariant symmetric [alpha]-stable Lévy processes and rotationally invariant symmetric truncated [alpha]-stable Lévy processes, we obtain that the Harnack inequalities hold for rotationally invariant symmetric [alpha]-stable Lévy processes with [alpha][set membership, variant](0,2) and Ornstein-Uhlenbeck processes driven by rotationally invariant symmetric [alpha]-stable Lévy process, while the logarithmic Harnack inequalities are satisfied for rotationally invariant symmetric truncated [alpha]-stable Lévy processes.

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  • Wang, Jian, 2011. "Harnack inequalities for Ornstein-Uhlenbeck processes driven by Lévy processes," Statistics & Probability Letters, Elsevier, vol. 81(9), pages 1436-1444, September.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:9:p:1436-1444
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    References listed on IDEAS

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    1. 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.
    2. Wang, Feng-Yu, 2011. "Gradient estimate for Ornstein-Uhlenbeck jump processes," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 466-478, March.
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