TY - JOUR A1 - Lie, Han Cheng A1 - Sullivan, T. J. A1 - Stuart, Andrew T1 - Strong convergence rates of probabilistic integrators for ordinary differential equations JF - Statistics and Computing N2 - Probabilistic integration of a continuous dynamical system is a way of systematically introducing model error, at scales no larger than errors inroduced by standard numerical discretisation, in order to enable thorough exploration of possible responses of the system to inputs. It is thus a potentially useful approach in a number of applications such as forward uncertainty quantification, inverse problems, and data assimilation. We extend the convergence analysis of probabilistic integrators for deterministic ordinary differential equations, as proposed by Conrad et al.\ (\textit{Stat.\ Comput.}, 2016), to establish mean-square convergence in the uniform norm on discrete- or continuous-time solutions under relaxed regularity assumptions on the driving vector fields and their induced flows. Specifically, we show that randomised high-order integrators for globally Lipschitz flows and randomised Euler integrators for dissipative vector fields with polynomially-bounded local Lipschitz constants all have the same mean-square convergence rate as their deterministic counterparts, provided that the variance of the integration noise is not of higher order than the corresponding deterministic integrator. Y1 - 2019 U6 - https://doi.org/10.1007/s11222-019-09898-6 VL - 29 IS - 6 SP - 1265 EP - 1283 ER - TY - JOUR A1 - Huisinga, Wilhelm A1 - Schütte, Christof A1 - Stuart, Andrew T1 - Extracting Macroscopic Stochastic Dynamics JF - Comm. Pure Appl. Math. Y1 - 2003 UR - http://publications.imp.fu-berlin.de/72/ U6 - https://doi.org/10.1002/cpa.10057 VL - 56 IS - 2 SP - 234 EP - 269 ER - TY - JOUR A1 - Walter, J. A1 - Schütte, Christof A1 - Pavliotis, G. A1 - Stuart, Andrew T1 - Averaging of Stochastic Differential Equations JF - preprint Y1 - 2004 UR - http://publications.imp.fu-berlin.de/63/ ER -