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Research Center BiBoS

 


Research Center BiBoS


Bielefeld-Bonn-Stochastics

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 Research Group Spectral
      analysis and stochastic
      dynamics
 

 University of Bielefeld
 Faculty of Physics
 Theoretical Physics
 Mathematical Physics
 

 University of Bonn
 Faculty of Mathematics
      and Natural Sciences
 Institute of Applied
      Mathematics
 Probability Theory
      and Statistics
 IZKS

Research

From 1984 to 1988 BiBoS was supported by the "Volkswagen-Stiftung" through a granting of DM 1,500,00 apart from the regular programmes. Since February 1988 it is financed among others by the DFG.

Main Research Activities

In the different fields of science and technology one has to deal with "irrgeluar" phenomena, which develop under the influence of coincidental "disturbances" and thus are at most accessible through a statistical description. Applications can be found wherever temporal courses are influenced by statistical factors. Those fields comprise

  • Mathematics (dynamical systems, differential geometry, analysis, discrete mathematics, statistics)
  • Physics
  • Biology and Sociology (population dynamics)
  • Ecology
  • Economics (stochastic optimal control)
  • Operations Research, System Theory (dynamical programming)
  • Engineering (stability tests, accelerated endurance tests)
  • Signal and Pattern Recognition (observation and piloting of projectiles and many other things)
  • Chemistry (diffusion reactions)
  • Electronics (filters)
  • Geography (weather forecasts, oceanography)
  • Medicine (epidemiology, immunology)
  • Geology (temporal sequences)
  • Neuroinformatics (neural networks)

Research Activities

White Noise Analysis reached an important stage by the publication of its first monograph ("White Noise", Hida, Kuo, Potthoff, Streit, Kluwer 1993). The further extension of the theory aimed at

  • general Gaussian analysis
  • general Gelfand tripels
  • non Gaussian analysis

On part of the applications, process is made at the theory of Feynman path integrals and at a better understanding of self intersection local times by its chaos development

The investigation of the structure and dynamics of complex systems has been continued with. The further extension of the theory aimed at

  • percolation theory
  • selforganized criticality
  • symbolic dynamics
  • structuring of neural networks

Under the term Event Enhanced Quantum Theory (EEQT) the standard formalism of the QUantum Theory has been extended. EEQT provides an algorithm for the simulation of experimental temporal sequences of individual quantum objects.

The common theory of infinite dimensional stochastical processes has been extended (extension of the common theory of nonsymmetrical Dirichlet forms, processes on loop spaces and other infinite dimensional manifolds).

Applications on the scrutiny of the stochastical dynamics (infinite dimensional spin systems, stochastic quantisation of fields, stochastic PDE's) have been investigated. Progress has also been made at the construction of Markov Fields and Quantum Fields on manifolds. Further applications comprise

  • classical and quantum-statistical mechanics
  • Physics of Polymers
  • stochastical financial markets
  • neural networks
  • dynamical systems
 
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