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R. Kupferman, Grigorios A. Pavliotis, Andrew M. StuartIto versus Stratonovich white noise limits for systems with inertia and colored multiplicative noise.We consider the dynamics of systems in the presence of inertia and colored multiplicative noise. We study the limit where the particle relaxation time and the correlation time of the noise both tend to zero. We show that the limiting equation for the particle position depends on the magnitude of the particle relaxation time relative to the noise correlation time. In particular, the limiting equation should be interpreted either in the Ito or Stratonovich sense, with a crossover occurring when the two fast time scales are of comparable magnitude. At the crossover the limiting stochastic differential equation is neither of Ito nor of Stratonovich type. Our findings are supported by numerical simulations.Bibliographical note: |