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Grigorios A. Pavliotis, Andrew M. StuartWhite noise limits for inertial particles in a random field.In this paper we present a rigorous analysis of various scaling limits related to the motion of an inertial particle in a Gaussian random field. The mathematical model comprises Stokes's law for the particle motion and an infinite dimensional Ornstein-Uhlenbeck process for the fluid velocity field. All of the scaling limits studied lead to a white noise limit for the fluid velocity, which balances particle inertia and/or friction terms. Strong convergence methods are used to justify the limiting equations. Apart from the fact that the rigorously derived limiting equations are of physical interest for the concrete problem under investigation, the methodology developed may also prove useful in the study of various other asymptotic problems for stochastic differential equations in infinite dimensions.Bibliographical note: |