Statisticians vs. stochasticians?

A person who does statistics is a statistician. What is a person called who does stochastics (or stochastic modelling)? Searching for "stochastician" yields almost no results (< 1000) compared to 19 million results when searching for "statistician".

Solution 1:

• If there were a profession or identity for someone who does a thing called 'stochastics' all day long, then yes you would call them a 'stochastician'. The term is a regular felicitous composition, similar to mathematician from mathematics and statistician from statistics.
• There are many people who do statistics as a full-time profession, and very few (if any at all) whose primary task in life is to perform stochastic things (like stochastic modeling. Stochastics is mostly a side tool for many technical professions but not a full-time goal. This accounts for the rare use of the term 'stochastician'.

...which is all to say that if you were forced to make a single word for the activity out of the performance of stochastic procedure, then 'stochastician' is the proper term. It's just that nobody does that.

It is most likely that it would sound better, instead of trying to force 'stochastician', to use the primary profession as a noun and then describe the person as using stochastics.

TL;DR Yes, 'stochastician' is a viable word but you shouldn't use it. Instead say

To study the effects of colliding galaxies, we're hired a newly graduated cosmologist to run all the simulations.