Harnack Inequalities for G-SDEs with Multiplicative Noise - Yang, Fen-Fen (Communications in mathematics and statistics, 2024)
The Harnack inequality for stochastic differential equation driven by G -Brownian motion with multiplicative noise is derived by means of the coupling by change of measure, which extends the corresponding results derived in Wang (Probab. Theory Related Fields 109:417–424) under the linear expectation. Moreover, we generalize the gradient estimate under nonlinear expectation appeared in Song (Sci. China Math. 64:1093–1108).