30 citations · 49 across the 7 of their papers we have counts for
5 papers · 1 filter
On optimal error rates for strong approximation of SDEs with a drift coefficient of fractional Sobolev regularity
Simon Ellinger, Thomas Müller-Gronbach, Larisa Yaroslavtseva
We study strong approximation of scalar additive noise driven stochastic differential equations (SDEs) at time point in the case that the drift coefficient is bounded and has S…
On the complexity of strong approximation of stochastic differential equations with a non-Lipschitz drift coefficient
T. Müller-Gronbach, L. Yaroslavtseva
We survey recent developments in the field of complexity of pathwise approximation in -th mean of the solution of a stochastic differential equation at the final time based on f…
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
Arnulf Jentzen, Benno Kuckuck, Thomas Müller-Gronbach +1
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 driv…
On the strong regularity of degenerate additive noise driven stochastic differential equations with respect to their initial values
Arnulf Jentzen, Benno Kuckuck, Thomas Müller-Gronbach +1
Recently in [M. Hairer, M. Hutzenthaler, and A. Jentzen, Ann. Probab. 43, 2 (2015), 468--527] and [A. Jentzen, T. Müller-Gronbach, and L. Yaroslavtseva, Commun. Math. Sci. 14, 6 (2…
General multilevel adaptations for stochastic approximation algorithms
Steffen Dereich, Thomas Mueller-Gronbach
In this article we present and analyse new multilevel adaptations of stochastic approximation algorithms for the computation of a zero of a function def…