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math.PR2020★ 3 cited
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…
math.PR2020
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…