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Journal of Statistical Physics

, Volume 141, Issue 1, pp 158–178 | Cite as

Vlasov Scaling for Stochastic Dynamics of Continuous Systems

  • Dmitri Finkelshtein
  • Yuri Kondratiev
  • Oleksandr Kutoviy
Article

Abstract

We describe a general derivation scheme for the Vlasov-type equations for Markov evolutions of particle systems in continuum. This scheme is based on a proper scaling of corresponding Markov generators and has an algorithmic realization in terms of related hierarchical chains of correlation functions equations. Several examples of realization of the proposed approach in particular models are presented.

Keywords

Continuous systems Vlasov scaling Vlasov equation Markov evolution Spatial birth-and-death processes Spatial hopping processes Correlation functions Scaling limits 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Dmitri Finkelshtein
    • 1
  • Yuri Kondratiev
    • 2
  • Oleksandr Kutoviy
    • 2
  1. 1.Institute of MathematicsNational Academy of Sciences of UkraineKyivUkraine
  2. 2.Fakultät für MathematikUniversität BielefeldBielefeldGermany

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