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A law of large numbers for moderately interacting diffusion processes. (English) Zbl 0549.60071
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.

MSC:
60J60 Diffusion processes
60K35 Interacting random processes; statistical mechanics type models; percolation theory
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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