38.94289904398774, -92.32798227119446

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Following Giovanni Volpe and Jan Wehr (2016 Rep. Prog. Phys. 79 053901), we analyze a minimal discrete-time dynamical system that models a colloid in a homogenous fluid (far from the boundary). In the presence of a boundary-induced diffusion gradient, the most obvious generalization of the model fails to exhibit the expected behavior. We show that this generalization approximates the Itô integral, while the correct dynamics of a near-equilibrium system are captured by the so-called "anti-Itô" model.

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