Foundations of Stochastic Mechanics
Stochastic mechanics is based on the hypothesis that all matter is subject to random fluctuations in position that are modified by the interactions that characterize a given system.
In my current opinion, there are three main fundamental papers that lay the groundwork for numerical stochastic mechanics. These are not by any means the only important papers, just some of the key early ideas that have shaped my thought. The first two articles were published in the German scientific literature, and the third much later in the US. Below is a timeline with brief descriptions and links to the original and translated articles.
Reading
1933
Fürth published an article on a probabilistic interpretation of quantum mechanics in pre-war German scientific literature. The original article is linked here, and a freely available English translation is linked here, and here, as well as a published open access version. Fürth established an analogy between quantum and diffusion processes by connecting Brownian motion and the Schrödinger equation.
1966
Nelson wrote "derivation of the Schödinger equation from Newtonian Mechanics" and established an analytical connection between classical and stochastic mechanics that a can be used to model real systems without requiring a previously calculated wave function. The original article is linked here.