The Langevin equation is a stochastic differential equation for the velocity of a Brownian particle. In this sense, it can be considered as a physically improved counterpart of the Wiener process, the velocity of which can only be defined as a stochastic distribution. On the contrary, the velocity of the Langevin model is a function valued stochastic process, what allows to calculate the kinetic energy of the Brownian particle. In fact, this calculation has been employed as a benchmark in the history of the classical Itô vs Stratonovich dilemma. Based on it, among other arguments, there appeared in the physical literature a clear preference for the use of the Stratonovich stochastic integral, at least in this type of context. However, it is possible to prove that the resulting Stratonovich stochastic differential equation admits an uncountable number of solutions. On the contrary, the use of Itô stochastic calculus leads to a unique solution, which turns out to be the right physical solution of the problem. This mathematical fact allows us to rethink the usual conclusions that seem to derive from the traditional approach to the Itô vs Stratonovich dilemma.
