Description

Leader of the group Scientific Computing: Daan Crommelin.

The SC groups develops efficient mathematical methods to simulate and predict real-world phenomena with inherent uncertainties. Such uncertainties arise from e.g. uncertain model parameters, chaotic dynamics or intrinsic randomness, and can have major impact on model outputs and predictions. Our work is targeted in particular at applications in climate, energy, finance and biology. In these vital areas, the ability to assess uncertainties and their impact on model predictions is of paramount importance. Expertise in the SC group includes uncertainty quantification, data assimilation, stochastic multiscale modeling and risk assessment. The availability of data to inform and improve simulations and predictions, for example through learning and data-driven modeling, plays an important role in our research.

 

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Probability Seminar Jonas Kremer (Bergische Universität Wuppertal)

  • 2018-12-14T11:00:00+01:00
  • 2018-12-14T12:00:00+01:00
December 14 Friday

Start: 2018-12-14 11:00:00+01:00 End: 2018-12-14 12:00:00+01:00

CWI, room L120

In this talk we study stochastic stability properties of affine processes. An affine process with state space $\mathbb{R}_{\geq0}^m\times\mathbb{R}^n$, where $m,\thinspace n\in\mathbb{Z}_{\geq0}$ with $m+n>0$, is a time-homogeneous Markov process $(X_t)_{t\geq0}$ taking values in $\mathbb{R}_{\geq0}^m\times\mathbb{R}^n$, whose $\log$-characteristic function depends in an affine way on the initial value of the process, that is, there exist functions $\phi$ and $\psi=(\psi_1,\ldots,\psi_{m+n})$ such that
\[\mathbb{E}\left.\left[\mathrm{e}^{\langle u,X_t\rangle}\thinspace\right\vert\thinspace X_0=x\right]
= \exp\left(\phi(t,u)+\langle \psi(t,u),x\rangle\right),\] for all $u\in\mathrm{i}\mathbb{R}^{m+n}$, $t\geq0$, and $x\in\mathbb{R}_{\geq0}^m\times\mathbb{R}^n$. We provide sufficient conditions for the existence of limiting distribution of a conservative affine process. Our main theorem extends and unifies some known results for OU-type processes on $\mathbb{R}^{n}$ and one-dimensional CBI processes (with state space $\mathbb{R}_{\geqslant0}$). Finally, we present some results on the (exponential) ergodicity with respect to the Wasserstein distance and total-variation distance for interesting subclasses of affine processes.

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Current projects with external funding

  • Accurate prediction of slugs in multiphase pipe flow simulation for improved oil and gas production
  • Geometric Structure and Data Assimilation
  • Probabilistic Uncertainty Assessments in Energy-Related Problems
  • Towards cloud-resolving climate simulations
  • Uncertainty Quantication in Hydraulic Fracturing using Multi-Level Monte Carlo and Multigrid
  • Excellence in Uncertainty Reduction of Offshore Wind Systems (EUROS)
  • Efficient numerical methods for deformable porous media. Application to carbon dioxide storage (PORO SOS)
  • Rare Event Simulation for Climate Extremes (RESClim)
  • Sloshing of Liquefied Natural Gas: subproject Variability (14-10-project2) (SLING)
  • Verified Exascale Computing for Multiscale Applications (VECMA)
  • Applied mathematics for risk measures in finance and insurance, in the wake of the crisis (WAKEUPCALL)

Related partners

  • FOM
  • Max Planck Institute for Informatics
  • Shell, Amsterdam
  • Vortech
  • Bull Sas
  • CBK Sci Con Ltd
  • Bayerische Akademie der Wissenschaften
  • Instytut Chemii Bioorganicznej Polskiej Akademii Nauk
  • Rijksuniversiteit Groningen
  • Technische Universiteit Eindhoven
  • Technische Universiteit Delft
  • Brunel University London
  • University College London
  • Universiteit van Amsterdam