Abstract

Given second-order Ito stochastic equations, we construct almost surely equivalent stochastic equations of the Lagrangian structure. We establish the conditions for the direct and indirect analytical representations of the Lagrangian in the presence of random perturbations. The results obtained are illustrated by examples.

中文翻译：

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随机亥姆霍兹问题和几乎肯定收敛

 抽象的

给定二阶伊藤随机方程，我们几乎可以肯定地构造拉格朗日结构的等价随机方程。我们建立了在存在随机扰动的情况下拉格朗日的直接和间接分析表示的条件。所获得的结果通过实例进行说明。