Counterexamples to local Lipschitz and local Hölder continuity with respect to the initial values for additive noise driven SDEs with smooth drift coefficient functions with at most polynomially growing derivatives

Abstract

In the recent article [A. Jentzen, B. Kuckuck, T. Müller-Gronbach, and L. Yaroslavtseva, arXiv:1904.05963 (2019)] it has been proved that the solutions to every additive noise driven stochastic differential equation (SDE) which has a drift coefficient function with at most polynomially growing first order partial derivatives and which admits a