Cerrai, SandraSalins, Michael2019-03-072019-03-072017-01-01Sandra Cerrai, Michael Salins. 2017. "On the Smoluchowski-Kramers approximation for a system with infinite degrees of freedom exposed to a magnetic field." STOCHASTIC PROCESSES AND THEIR APPLICATIONS, Volume 127, Issue 1, pp. 273 - 303 (31). https://doi.org/10.1016/j.spa.2016.06.0080304-41491879-209Xhttps://hdl.handle.net/2144/34256We study the validity of the so-called Smoluchowski–Kramers approximation for a two dimensional system of stochastic partial differential equations, subject to a constant magnetic field. Since the small mass limit does not yield to the solution of the corresponding first order system, we regularize our problem by adding a small friction. We show that in this case the Smoluchowski–Kramers approximation holds. We also give a justification of the regularization, by showing that the regularized problems provide a good approximation to the original ones.p. 273 - 303en-USScience & technologyPhysical sciencesStatistics & probabilityMathematicsStochastic partial differential equationsSmoluchowski-Kramers approximationMagnetic fieldSmall mass asymptoticsCharged-particleStatisticsBanking, finance and investmentArticle10.1016/j.spa.2016.06.008