30 citations · 49 across the 7 of their papers we have counts for
10 papers
On the performance of the Euler-Maruyama scheme for multidimensional SDEs with discontinuous drift coefficient
Thomas Müller-Gronbach, Christopher Rauhögger, Larisa Yaroslavtseva
We study strong approximation of -dimensional stochastic differential equations (SDEs) with a discontinuous drift coefficient. More precisely, we essentially assume that the dri…
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…
On the performance of the Euler-Maruyama scheme for SDEs with discontinuous drift coefficient
Thomas Müller-Gronbach, Larisa Yaroslavtseva
Recently a lot of effort has been invested to analyze the -error of the Euler-Maruyama scheme in the case of stochastic differential equations (SDEs) with a drift coefficient…
Lower Error Bounds for Strong Approximation of Scalar SDEs with non-Lipschitzian Coefficients
Mario Hefter, André Herzwurm, Thomas Müller-Gronbach
We study pathwise approximation of scalar stochastic differential equations at a single time point or globally in time by means of methods that are based on finitely many observati…
On hard quadrature problems for marginal distributions of SDEs with bounded smooth coefficients
Thomas Müller-Gronbach, Larisa Yaroslavtseva
In recent work of Hairer, Hutzenthaler and Jentzen, see [9], a stochastic differential equation (SDE) with infinitely often differentiable and bounded coefficients was constructed…
On stochastic differential equations with arbitrary slow convergence rates for strong approximation
Arnulf Jentzen, Thomas Müller-Gronbach, Larisa Yaroslavtseva
In the recent article [Hairer, M., Hutzenthaler, M., Jentzen, A., Loss of regularity for Kolmogorov equations, Ann. Probab. 43 (2015), no. 2, 468--527] it has been shown that there…
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…