Summary
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.
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To the Memory of the late Professor Gishiro Maruýama
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Nagasawa, M., Tanaka, H. Diffusion with interactions and collisions between coloured particles and the propagation of chaos. Probab. Th. Rel. Fields 74, 161–198 (1987). https://doi.org/10.1007/BF00569988
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DOI: https://doi.org/10.1007/BF00569988
Keywords
- Colour
- Reflection
- Differential Equation
- Stochastic Process
- Probability Theory