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Humboldt-Universität zu Berlin - Faculty of Mathematics and Natural Sciences - RTG1845

 

Dynamics

 

The mathematical models of this domain arise for instance from high frequency financial or climate data, and are crucial for processes in finance, physics and biology investigated in the other two research domains of the RTG. We both study their dynamics and calibrate them to reality through statistical inference. The description of the models' dynamics

leads to the main objects of stochastic analysis: stochastic (partial, delayed) differential equations, driven by Gaussian or Lévy processes, or more generally affine processes or semi-martingales, or in a still more general context by rough paths. Noise induced phenomena modeled by such equations are related to systems' invariant structures, in particular local attractors and stable regimes, which become random and meta-stable through perturbation by noise. The faculty members with a focus of activity in this domain are P. Friz, P. Imkeller, N. Perkowski, M. Reiß, and M. Scheutzow.

 

Main research fields

 

  • stochastic flows
  • ergodic theory and meta-stability
  • rough paths and stochastic analysis
  • quantization of stochastic processes
  • nonparametric inference for processes with jumps
  • inference for climate time series