If that text is about stochastic mechanics and QM, shouldn't it have an introduction to the ideas behind a Wiener process, i.e. a fluctuating driving force being added to the fundamental equations at the quantum level?


It would be interesting to get some clarification here. IMO the concept of stochastic mechanics is essentially that of a stochastic process or Markov process where the future is independent of the present.

Moreover, there's also some indication that Stochastic Mechanics defines an alternative approach to understanding QM

> **Stochastic mechanics**
>This interpretation, or perhaps explanation, of quantum mechanics leaves logic intact but adds a new physical process. The modern and enduring branch of stochastic mechanics began with a 1966 paper by Edward Nelson that begins boldly:

> “We shall attempt to show in this paper that the radical departure from classical physics produced by the introduction of quantum mechanics forty years ago was unnecessary.”

> The main result of the paper is impressive: the author derives the Schrödinger equation, the central equation of quantum mechanics, by assuming that particles are subject to a rapidly fluctuating random force. Microscopic particles such as electrons are therefore described as executing something similar to Brownian motion, and Nelson uses much of the related mathematics from statistical physics in his derivation.

> Since Nelson’s paper, the field has grown steadily and attracted a large community of researchers. Some of its intriguing successes include an explanation for quantized angular momentum (“spin”), quantum statistics, and the famous two-slit experiment. However, stochastic mechanics is still far from replacing the Copenhagen Interpretation or conventional quantum mechanics. It includes what appears to be an unphysical instantaneous action at a distance and gives incorrect predictions for certain types of measurements. But its proponents have not given up. As Nelson asks in a review of the subject, “How can a theory to be so right and yet so wrong?”

from this article, https://arstechnica.com/science/2017/07/a-brief-history-of-quantum-alternatives/, the author of which I just had a twitter discussion this morning. That may explain why I was confused by the use of the phrase Stochastic Mechanics, which apparently may not be part of the consensus vocabulary.