Acta Mathematica Vietnamica
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Smoluchowski–Kramers Approximation for the Derivative of Solutions
Nguyen Van Tanpp. 201-218
Abstract
In this paper, we provide a new property for the Smoluchowski-Kramers approximation of stochastic differential equations. We prove the convergence of the derivative of solutions with respect to the initial condition (when the mass of particles tends to zero). We then use the techniques of Malliavin calculus to obtain an explicit Berry-Esseen error bound for the rate of convergence.