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Strong Feller property for one-dimensional Lévy processes driven stochastic differential equations with Hölder continuous coefficients

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  • Zhang, Hua

Abstract

In this paper, under the assumption of Hölder continuous coefficients, we prove the strong Feller property for the solution to one-dimensional Lévy processes driven stochastic differential equations. Our proof is based on the tools of Yamada–Watanabe approximation technique, Girsanov’s theorem and coupling method. Using this approach, the continuous dependence on initial data for the same equations can be also obtained, which is of independent interest.

Suggested Citation

  • Zhang, Hua, 2021. "Strong Feller property for one-dimensional Lévy processes driven stochastic differential equations with Hölder continuous coefficients," Statistics & Probability Letters, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:stapro:v:169:y:2021:i:c:s0167715220302777
    DOI: 10.1016/j.spl.2020.108974
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    References listed on IDEAS

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    1. Wang, Linlin & Xie, Longjie & Zhang, Xicheng, 2015. "Derivative formulae for SDEs driven by multiplicative α-stable-like processes," Stochastic Processes and their Applications, Elsevier, vol. 125(3), pages 867-885.
    2. Zhang, Xicheng, 2013. "Derivative formulas and gradient estimates for SDEs driven by α-stable processes," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1213-1228.
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