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- A.-M. Matache, T. von Petersdorff, C. Schwab
- 2002

A partial integro-differential equation (PIDE) ∂ t u + A[u] = 0 for European contracts on assets with general jump-diffusion price process of Lévy type is derived. The PIDE is localized to bounded domains and the error due to this localization is estimated. The localized PIDE is discretized by the θ-scheme in time and a wavelet Galerkin method with N… (More)

- Annalisa Buffa, Ralf Hiptmair, Tobias von Petersdorff, Christoph Schwab
- Numerische Mathematik
- 2003

- Tobias von Petersdorff, Christoph Schwab
- SIAM J. Numerical Analysis
- 2003

We consider a Galerkin method for an elliptic pseudodifferential operator of order zero on a two-dimensional manifold. We use piecewise linear discontinuous trial functions on a triangular mesh and describe an orthonormal wavelet basis. Using this basis we can compress the stiffness matrix from N 2 to O(N log N) nonzero entries and still obtain (up to log N… (More)

- Ricardo H. Nochetto, Tobias von Petersdorff, Chen-Song Zhang
- Numerische Mathematik
- 2010

We consider elliptic and parabolic variational equations and inequalities governed by integro-differential operators of order 2s ∈ (0, 2]. Our main motivation is the pricing of European or American options under Lévy processes, in particular pure jump processes or jump diffusion processes with tempered stable processes. The problem is discretized using… (More)

Motivated by the pricing of American options for baskets we consider a parabolic varia-tional inequality in a bounded polyhedral domain Ω ⊂ R d with a continuous piecewise smooth obstacle. We formulate a fully discrete method by using piecewise linear finite elements in space and the backward Euler method in time. We define an a posteriori error estimator… (More)

Notation: For two sets A, B we write A ⊂ B iff x ∈ A =⇒ x ∈ B. So A ⊂ A is true. Some people use the notation " ⊆ " instead.

- F König, C von Hippel, T Petersdorff, M Neuhöffer-Weiss, M Wolfersdorf, W P Kaschka
- Neuropsychobiology
- 2001

In an open prospective study, 26 patients with delusional depression (mood-congruent psychotic features: DSM-IV 296.4) were treated over 5 weeks with a combination of SSRI (citalopram, n = 22, or paroxetine, n = 4) and the neuroleptic olanzapine. The course of therapy was evaluated with the Hamilton depression scale (HAMD). Not only the total HAMD score,… (More)

- F König, C von Hippel, T Petersdorff, W Kaschka
- Acta medica Austriaca
- 1999

Whereas clinical relevant hypo- as well as hyperthyreosis are strongly suspected to induce psychiatric symptoms, there is a controversy about the relevance of only subclinical and autoimmune findings. We found autoantibodies (MAK, TAK, TRAK) in a high percentage (100 out of 144 = 70%) in severely depressed inpatients. Also we found a Hashimoto thyreoiditis… (More)

We consider an integral equation obtained by the " direct method " for the Neumann problem on a polygonal domain which may contain slits, i.e., interior angles of 2π. By using a Galerkin method with piecewise linear functions on a suitable graded mesh one can obtain the optimal convergence rate h 3/2. Using a Gauss solver for the arising linear system would… (More)