1.8k citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- ETH ZurichCH99 papers
- University of MünsterDE18 papers
- University of PaviaIT9 papers
- University of ViennaAT9 papers
- University of Duisburg-EssenDE7 papers
- Chinese University of Hong Kong, ShenzhenCN6 papers
- Shenzhen Research Institute of Big DataCN6 papers
- University of Maryland, College ParkUS6 papers
- Princeton UniversityUS5 papers
- TU WienAT5 papers
- Austrian Academy of SciencesAT4 papers
- Chalmers University of TechnologySE4 papers
7 papers · 1 filter
Approximation methods for piecewise deterministic Markov processes and their costs
Peter Kritzer, Gunther Leobacher, Michaela Szölgyenyi +1
In this paper, we analyse piecewise deterministic Markov processes, as introduced in Davis (1984). Many models in insurance mathematics can be formulated in terms of the general co…
Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen-Cahn equations
Sebastian Becker, Benjamin Gess, Arnulf Jentzen +1
The scientific literature contains a number of numerical approximation results for stochastic partial differential equations (SPDEs) with superlinearly growing nonlinearities but,…
The rational SPDE approach for Gaussian random fields with general smoothness
David Bolin, Kristin Kirchner
A popular approach for modeling and inference in spatial statistics is to represent Gaussian random fields as solutions to stochastic partial differential equations (SPDEs) of the…
On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations
Weinan E, Martin Hutzenthaler, Arnulf Jentzen +1
Parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) are key ingredients in a number of models in physics and financial engineerin…
Tensor FEM for spectral fractional diffusion
Lehel Banjai, Jens M. Melenk, Ricardo H. Nochetto +3
We design and analyze several Finite Element Methods (FEMs) applied to the Caffarelli-Silvestre extension that localizes the fractional powers of symmetric, coercive, linear ellipt…
Solving high-dimensional partial differential equations using deep learning
Jiequn Han, Arnulf Jentzen, Weinan E
Developing algorithms for solving high-dimensional partial differential equations (PDEs) has been an exceedingly difficult task for a long time, due to the notoriously difficult pr…
On arbitrarily slow convergence rates for strong numerical approximations of Cox-Ingersoll-Ross processes and squared Bessel processes
Mario Hefter, Arnulf Jentzen
Cox-Ingersoll-Ross (CIR) processes are extensively used in state-of-the-art models for the approximative pricing of financial derivatives. In particular, CIR processes are day afte…