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- Jakob Creutzig, Steffen Dereich, Thomas MÃ¼ller-Gronbach, Klaus Ritter
- Foundations of Computational Mathematics
- 2009

We study numerical integration of Lipschitz functionals on a Banach space by means of deterministic and randomized (Monte Carlo) algorithms. This quadrature problem is shown to be closely related toâ€¦ (More)

- Steffen Dereich, Felix Heidenreich
- 2010

This article introduces and analyzes multilevel Monte Carlo schemes for the evaluation of the expectation E[f(Y )], where Y = (Yt)tâˆˆ[0,1] is a solution of a stochastic differential equation driven byâ€¦ (More)

- Steffen Dereich
- 2003

In this thesis, we study the high resolution coding problem for stochastic processes. The general coding problem concerns the finding of a good representation of a random signal, the original, withinâ€¦ (More)

- Steffen Dereich
- 2008

We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit lawâ€¦ (More)

The background for the general mathematical link between utility and information theory investigated in this paper is a simple financial market model with two kinds of small traders: less informedâ€¦ (More)

- Steffen Dereich
- 2006

We investigate the high resolution quantization and entropy coding problem for solutions of stochastic differential equations under supremum norm distortion. Tight asymptotic formulas are found underâ€¦ (More)

- Steffen Dereich
- 2005

We establish the precise asymptotics of the quantization and entropy coding errors for fractional Brownian motion with respect to the supremum norm and L[0, 1]-norm distortions. We show that allâ€¦ (More)

We consider the one-sided exit problem for (fractionally) integrated random walks and LÃ©vy processes. We prove that the rate of decrease of the non-exit probability â€“ the so-called survival exponentâ€¦ (More)

We study the small deviation problem log P(suptâˆˆ[0,1] |Xt| 6 Îµ), as Îµ â†’ 0, for general LÃ©vy processes X . The techniques enable us to determine the asymptotic rate for general real-valued LÃ©vyâ€¦ (More)

- Steffen Dereich, Michael Scheutzow, Reik Schottstedt
- 2012

In this article, we study the approximation of a probability measure Î¼ on Rd by its empirical measure Î¼Ì‚N interpreted as a random quantization. As error criterion we consider an averaged pth momentâ€¦ (More)