30 citations · 46 across the 12 of their papers we have counts for
15 papers
Sharp lower error bounds for strong approximation of SDEs with a drift coefficient of Hölder or Sobolev regularity using a Weierstraß scale
Simon Ellinger, Thomas Müller-Gronbach, Larisa Yaroslavtseva
We study strong approximation of solutions of SDEs with bounded -Hölder continuous drift coefficient and constant diffusion coefficient at time point . Recently, it was shown…
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…
Existence, uniqueness and approximation of solutions of SDEs with superlinear coefficients in the presence of discontinuities of the drift coefficient
Thomas Müller-Gronbach, Sotirios Sabanis, Larisa Yaroslavtseva
Existence, uniqueness, and -approximation results are presented for scalar stochastic differential equations (SDEs) by considering the case where, the drift coefficient has fi…
An adaptive strong order 1 method for SDEs with discontinuous drift coefficient
Larisa Yaroslavtseva
In recent years, an intensive study of strong approximation of stochastic differential equations (SDEs) with a drift coefficient that may have discontinuities in space has begun. I…
Sharp lower error bounds for strong approximation of SDEs with discontinuous drift coefficient by coupling of noise
Thomas Müller-Gronbach, Larisa Yaroslavtseva
In the past decade, an intensive study of strong approximation of stochastic differential equations (SDEs) with a drift coefficient that has discontinuities in space has begun. In…
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…
A strong order method for SDEs with discontinuous drift coefficient
Thomas Müller-Gronbach, Larisa Yaroslavtseva
In this paper we study strong approximation of the solution of a scalar stochastic differential equation (SDE) at the final time in the case when the drift coefficient may have dis…
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…
A note on strong approximation of SDEs with smooth coefficients that have at most linearly growing derivatives
Thomas Müller-Gronbach, Larisa Yaroslavtseva
Recently, it has been shown in [Jentzen, A., Müller-Gronbach, T., and Yaroslavtseva, L., Commun. Math. Sci., 14, 2016] that there exists a system of autonomous stochastic different…
On non-polynomial lower error bounds for adaptive strong approximation of SDEs
Larisa Yaroslavtseva
Recently, it has been shown in [Hairer, M., Hutzenthaler, M., Jentzen, A., Loss of regularity for Kolmogorov equations, Ann. Probab. 43, 2 (2015), 468--527] that there exists a sys…
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…