Summary
We consider two special models of interacting diffusion processes, and derive in the limit, as the number of different processes tends to infinity and the interaction is rescaled in a suitable (“moderate”) way, a law of large numbers for the empirical processes. As limit dynamics we obtain certain nonlinear diffusion equations.
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This work has been supported by the Deutsche Forschungsgemeinschaft.
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Oelschläger, K. A law of large numbers for moderately interacting diffusion processes. Z. Wahrscheinlichkeitstheorie verw Gebiete 69, 279–322 (1985). https://doi.org/10.1007/BF02450284
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DOI: https://doi.org/10.1007/BF02450284