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Sub-Markovian C 0-Semigroups Generated by Fractional Laplacian with Gradient Perturbation

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Abstract

We present a sufficient condition for fractional Laplacian with gradient perturbation to generate a sub-Markovian C 0-semigroup on \({L^1(\mathbb{R}^d, dx)}\). The condition also yields the ultracontractivity of the semigroup and an upper on-diagonal estimate of the associated transition kernel. Based on the subordination technique, the extension to general pure jump Lévy process with gradient perturbation is studied. As a direct application, we obtain sufficient conditions for the strong Feller property of stochastic differential equations driven by additive Lévy process.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Fujian Normal University, 350007, Fuzhou, P.R. China

    Jian Wang

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  1. Jian Wang
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Correspondence to Jian Wang.

Additional information

Financial supports through National Natural Science Foundation of China (No. 11201073) and the Program for New Century Excellent Talents in Universities of Fujian (No. JA11051 and JA12053) are gratefully acknowledged.

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Wang, J. Sub-Markovian C 0-Semigroups Generated by Fractional Laplacian with Gradient Perturbation. Integr. Equ. Oper. Theory 76, 151–161 (2013). https://doi.org/10.1007/s00020-013-2055-3

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  • DOI: https://doi.org/10.1007/s00020-013-2055-3

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