This Wikipedia page at least tries to explain the name as the stochastic interpretation of QM

> https://en.wikipedia.org/wiki/Stochastic_quantum_mechanics

> "Perhaps the most widely known theory where quantum mechanics is assumed to describe an inherently stochastic process was put forward by Edward Nelson [[6]](https://www.worldcat.org/title/dynamical-theories-of-brownian-motion-part-1/oclc/25799122) and is called stochastic mechanics. This was also developed by Davidson, Guerra, Ruggiero and others."

Nelson developed his "dynamical theory of Brownian motion" in 1966.

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And then there's this : https://archive.is/20170607120820/https://golem.ph.utexas.edu/category/2011/09/the_inconsistency_of_arithmeti.html

> https://en.wikipedia.org/wiki/Stochastic_quantum_mechanics

> "Perhaps the most widely known theory where quantum mechanics is assumed to describe an inherently stochastic process was put forward by Edward Nelson [[6]](https://www.worldcat.org/title/dynamical-theories-of-brownian-motion-part-1/oclc/25799122) and is called stochastic mechanics. This was also developed by Davidson, Guerra, Ruggiero and others."

Nelson developed his "dynamical theory of Brownian motion" in 1966.

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And then there's this : https://archive.is/20170607120820/https://golem.ph.utexas.edu/category/2011/09/the_inconsistency_of_arithmeti.html