We compute the kinetic energy of the Langevin particle using different approaches. We build stochastic differential equations that describe this physical quantity based on both the Ito and Stratonovich stochastic integrals. It is shown that the Ito equation possesses a unique solution whereas the Stratonovich one possesses infinitely many, all but one absent of physical meaning. We discuss how this fact matches with the existent discussion on the Ito vs Stratonovich dilemma and the apparent preference towards the Stratonovich interpretation in the physical literature.

中文翻译：

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朗之万粒子的动能

我们使用不同的方法计算朗之万粒子的动能。我们基于 Ito 和 Stratonovich 随机积分构建了描述该物理量的随机微分方程。结果表明，Ito 方程具有唯一解，而 Stratonovich 方程具有无限多个解，但只有一个没有物理意义。我们讨论了这一事实如何与现有的关于 Ito 与 Stratonovich 困境的讨论以及物理文献中对 Stratonovich 解释的明显偏好相匹配。