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- A. Neuenkirch, I. Nourdin, S. Tindel
- 2007

In this article, we illustrate the flexibility of the algebraic integration formalism introduced in M. Gubinelli (2004), Controlling Rough Paths, J. Funct. Anal. 216, 86-140, by establishing an existence and uniqueness result for delay equations driven by rough paths. We then apply our results to the case where the driving path is a fractional Brownian… (More)

- Peter E. Kloeden, Gabriel J. Lord, Andreas Neuenkirch, Tony Shardlow
- J. Computational Applied Mathematics
- 2011

We present an error analysis for a general semilinear stochastic evolution equation in d dimensions based on pathwise approximation. We discretize in space by a Fourier Galerkin method and in time by 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… (More)

- Arnulf Jentzen, Peter E. Kloeden, Andreas Neuenkirch
- Numerische Mathematik
- 2009

- BY STEFFEN DEREICH, ANDREAS NEUENKIRCH, LUKASZ SZPRUCH
- 2012

We analyse the strong approximation of the Cox–Ingersoll–Ross (CIR) process in the regime where the process does not hit zero by a positivity preserving drift-implicit Eulertype method. As an error criterion, we use the pth mean of the maximum distance between the CIR process and its approximation on a finite time interval. We show that under mild… (More)

- Andreas Neuenkirch, Lukasz Szpruch
- Numerische Mathematik
- 2014

In this paper, we derive the exact rate of convergence of some approximation schemes associated to scalar stochastic differential equations driven by a fractional Brownian motion with Hurst index H . We consider two cases. If H > 1/2, the exact rate of convergence of the Euler scheme is determined. We show that the error of the Euler scheme converges almost… (More)

- Andreas Neuenkirch
- J. Complexity
- 2006

From 23.09.12 to 28.09.12, the Dagstuhl Seminar 12391 Algorithms and Complexity for Continuous Problems was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the… (More)

- Peter E. Kloeden, Andreas Neuenkirch, Raffaella Pavani
- Annals OR
- 2011

- A. Neuenkirch, I. Nourdin, A. Rößler
- 2006

In this paper we consider a n-dimensional stochastic differential equation driven by a fractional Brownian motion with Hurst parameter H > 1/3. After solving this equation in a rather elementary way, following the approach of [10], we show how to obtain an expansion for E[f(Xt)] in terms of t, where X denotes the solution to the SDE and f : Rn → R is a… (More)