In the context of instanton method for stochastic system this paper purposes a modification of the arclength parametrization of the Hamilton’s equations allowing for an arbitrary instanton speed. The main results of the paper are: (i) it generalizes the parametrized Hamilton’s equations to any speed required. (ii) Corrects the parametric action on the occasion that the Hamiltonian is small but finite and how it adjusts to the probability density function (pdf). (iii) Improves instanton approximation to pdf by noise and propagator renormalization. As an application of the above set up we evaluate the instanton and predict the statistics of two models: Ornstein–Uhlenbeck and passive scalar gradients in a Lagrangian model for turbulence, namely the scalar gradient recent fluid deformation closure.

中文翻译：

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随机系统的参数汉密尔顿方程

在随机系统的瞬时量方法的背景下，本文旨在修改Hamilton方程的弧长参数化，以允许任意瞬时速度。本文的主要结果是：（i）将参数化的汉密尔顿方程推广到所需的任何速度。（ii）在哈密顿量较小但有限的情况下校正参数作用，以及如何调整其以适应概率密度函数（pdf）。（iii）通过噪声和传播子的重归一化将瞬时近似值提高到pdf。作为上述设置的应用，我们评估了瞬时值并预测了两种模型的统计量：湍流的拉格朗日模型中的Ornstein–Uhlenbeck和被动标量梯度，即标量梯度最近的流体变形闭合。