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<p>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.</p>

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Smoluchowski–Kramers Approximation for the Derivative of Solutions

  • 期刊论文

  • 发表日期：

    2026年7月23日

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  • Nguyen Van Tan

摘要

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.