Probability Theory and Related Fields

, Volume 74, Issue 2, pp 161–198 | Cite as

Diffusion with interactions and collisions between coloured particles and the propagation of chaos

  • Masao Nagasawa
  • Hiroshi Tanaka


One considers a system ofN particles on the real line which are of two different types (colours). Their dynamics is given by a stochastic differential equation with constant diffusion part; the drift felt by a particle of either type depends on the empirical measures of type 1 and 2 particles at every instant; further a reflection condition is imposed so that particles of different type are not allowed to cross each other. The article studies the Vlasov-McKean limit of the system asN→∞: propagation of chaos and an evolution equation for the limiting empirical measures is established, from where in particular an equation for the separating front between the two types follos.


Colour Reflection Differential Equation Stochastic Process Probability Theory 
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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Masao Nagasawa
    • 1
  • Hiroshi Tanaka
    • 2
  1. 1.Institut für Angewandte Mathematik der Universität ZürichZürichSwitzerland
  2. 2.Department of Mathematics, Faculty of Science and TechnologyKeio UniversityHiyoshi, YokohamaJapan

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