R. F\"urth's 1933 paper "On certain relations between classical Statistics and Quantum Mechanics" ["\"Uber einige Beziehungen zwischen klassischer Statistik und Quantenmechanik", $\mathit{\text{Zeitschrift}}\mathit{\text{f}}\ddot{\mathit{\text{u}}}\mathit{\text{r}}\mathit{\text{Physik,}}$ $\mathbf{\text{81}}$ 143-162]

We present a translation of the 1933 paper by R. F"urth in which a profound analogy between quantum fluctuations and Brownian motion is pointed out. This paper opened in some sense the way to the stochastic methods of quantization developed almost 30 years later by Edward Nelson and others.