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We consider a stochastic differential equation on R d with Lipschitz coefficients. We find a core for the infinitesimal generator of the corresponding Markov process. Some applications, in particular, to well-posedness of Fokker-Planck equations are given. 2000 Mathematics Subject Classification AMS: 60H10, 60J35, 47D07.doi:10.1063/1.3546077 fatcat:6rf7yguq45elxnicirbdpplnge