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Harnack inequality and gradient estimate for functional G-SDEs with degenerate noise

The authors would like to thank Doctor Xing Huang for corrections and helpful comments. This work was supported in part by NNSFC (Grant No. 12101390).

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  • In this paper, the Harnack and shift Harnack inequalities for functional G-SDEs with degenerate noise are derived by the method of coupling by change of measure. Moreover, the gradient estimate for the associated nonlinear semigroup $\bar{P}_t $ is obtained. All of the above results extend the existed results in linear expectation setting.

    Mathematics Subject Classification: 60H10, 60H15.


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