Andreas Neuenkirch
Goethe University Frankfurt
Network
Latest external collaboration on country level. Dive into details by clicking on the dots.
Publication
Featured researches published by Andreas Neuenkirch.
Numerische Mathematik | 2009
Arnulf Jentzen; Peter E. Kloeden; Andreas Neuenkirch
We study the approximation of stochastic differential equations on domains. For this, we introduce modified Itô–Taylor schemes, which preserve approximately the boundary domain of the equation under consideration. Assuming the existence of a unique non-exploding solution, we show that the modified Itô–Taylor scheme of order γ has pathwise convergence order γ − ε for arbitrary ε >xa00 as long as the coefficients of the equation are sufficiently differentiable. In particular, no global Lipschitz conditions for the coefficients and their derivatives are required. This applies for example to the so called square root diffusions.
Journal of Computational and Applied Mathematics | 2011
Peter E. Kloeden; Gabriel J. Lord; Andreas Neuenkirch; Tony Shardlow
We present an error analysis for the pathwise approximation of a general semilinear stochastic evolution equation in d dimensions. We discretise in space by a Galerkin method and in time by using a stochastic exponential integrator. We show that for spatially regular (smooth) noise the number of nodes needed for the noise can be reduced and that the rate of convergence degrades as the regularity of the noise reduces (and the noise becomes rougher).
Annals of Operations Research | 2011
Peter E. Kloeden; Andreas Neuenkirch; Raffaella Pavani
We adopt the multilevel Monte Carlo method introduced by M.xa0Giles (Multilevel Monte Carlo path simulation, Oper. Res. 56(3):607–617, 2008) to SDEs with additive fractional noise of Hurst parameter H>1/2. For the approximation of a Lipschitz functional of the terminal state of the SDE we construct a multilevel estimator based on the Euler scheme. This estimator achieves a prescribed root mean square error of order ε with a computational effort of order ε−2.
Annales De L Institut Henri Poincare-probabilites Et Statistiques | 2009
Andreas Neuenkirch; Ivan Nourdin; Andreas Rößler; Samy Tindel
In this article, we consider an n-dimensional stochastic differential equation driven by a fractional Brownian motion with Hurst parameterH >1/3. We derive an expansion for E[f (Xt )] in terms of t, where X denotes the solution to the SDE and f :Rn →R is a regular function. Comparing to F. Baudoin and L. Coutin, Stochastic Process. Appl. 117 (2007) 550-574, where the same problem is studied, we provide an improvement in three different directions: we are able to consider equations with drift, we parametrize our expansion with trees, which makes it easier to use, and we obtain a sharp estimate of the remainder for the case H >1/2.
Journal of Difference Equations and Applications | 2009
Peter E. Kloeden; Andreas Neuenkirch; Raffaella Pavani
It is shown that the synchronization of noisy dissipative systems is preserved when a drift-implicit Euler scheme is used for the discretization. In particular, in this case the order of discretization and synchronization can be exchanged.
Journal of Theoretical Probability | 2007
Andreas Neuenkirch; Ivan Nourdin
Electronic Journal of Probability | 2008
Andreas Neuenkirch; Ivan Nourdin; Samy Tindel
Applied Mathematics and Optimization | 2009
María J. Garrido-Atienza; Peter E. Kloeden; Andreas Neuenkirch
Stochastic Processes and their Applications | 2008
Andreas Neuenkirch
Stochastic Processes and their Applications | 2010
Andreas Neuenkirch; Samy Tindel; Jérémie Unterberger