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

Fen-Fen Yang

doi:10.3934/puqr.2022008

Article Contents

2022, Volume 7, Issue 2: 119-132. Doi: 10.3934/puqr.2022008

This issue Previous Article Path independence of the additive functionals for stochastic differential equations driven by G-lévy processes Next Article On the speed of convergence of Picard iterations of backward stochastic differential equations

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

Fen-Fen Yang

1.
Department of Mathematics, Shanghai University, Shanghai 200444, China

Received: December 15, 2021

Accepted: June 06, 2022

Early access: June 2022

Published: June 2022

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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Abstract

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.

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Mathematics Subject Classification: 60H10, 60H15.

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