On the strong regularity of degenerate additive noise driven stochastic differential equations with respect to their initial values (Q2033122)

This article is devoted to proving that if it satisfies a certain Lyapunov-type condition, an additive noise driven stochastic differential equation (SDE) whose drift function has partial derivatives with at most polynomial growth is at least logarithmically Hölder continuous in the initial value. This result can be used to establish convergence rates of numerical methods used to approximate the solutions of these SDEs.