A note on the G-Itô Formula and a comment on “Averaging Principle for SDEs of Neutral Type Driven by G-Brownian Motion”

Abstract

This is a comment on the paper Stoch. Dyn. 19(1) (2019) 1950004, http://doi.org/10.1142/S0219493719500047 ) titled “Averaging Principle for SDEs of Neutral Type Driven by G-Brownian Motion”, preceded by a note on the G-Itô formula. In the commented paper, the authors provided a wrong result and incorrect computations in their Theorem 4.1 and Appendix B, which probably result from the misapplication of the G-Itô Formula in the sublinear expectation theory. Hence, we provide a differential form of the G-Itô formula with a calculation table and the correct computation on the solution related to Theorem 4.1 of the commented paper.