Harnack Inequalities for G-SDEs with Multiplicative Noise

Abstract

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).

Keywords

Harnack inequality / Gradient estimate / Multiplicative noise / G-Brownian motion / SDEs

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Funding

Young Scientists Fund(11801406)