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Mild Solutions and Harnack Inequality for Functional Stochastic Partial Differential Equations with Dini Drift

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  • Xing Huang

    (Tianjin University)

  • Shao-Qin Zhang

    (Central University of Finance and Economics)

Abstract

The existence and uniqueness of a mild solution for a class of functional stochastic partial differential equations with multiplicative noise and a locally Dini continuous drift are proved. In addition, under a reasonable condition the solution is non-explosive. Moreover, Harnack inequalities are derived for the associated semigroup under certain global conditions, which is new even in the case without delay.

Suggested Citation

  • Xing Huang & Shao-Qin Zhang, 2019. "Mild Solutions and Harnack Inequality for Functional Stochastic Partial Differential Equations with Dini Drift," Journal of Theoretical Probability, Springer, vol. 32(1), pages 303-329, March.
    • Handle: RePEc:spr:jotpro:v:32:y:2019:i:1:d:10.1007_s10959-018-0830-4
    DOI: 10.1007/s10959-018-0830-4
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    References listed on IDEAS

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    1. T. E. Govindan, 2011. "Mild Solutions of Neutral Stochastic Partial Functional Differential Equations," International Journal of Stochastic Analysis, Hindawi, vol. 2011, pages 1-13, September.
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