I have never studied random processes, but in my baggage I carry only basic concepts of probability that can all be enclosed in the first chapter of this book https://www.springer.com/gp/book/9781475725391 (elementary probability theory). With this premise, I find myself having to deal with thermal noise for work. To this end I am trying to get an idea of what a random process is, and what I understand is this: given a space $(\Omega, \mathcal {A}, P)$ a random process is a set of different random variables, which I indicate as follows.
$$\{\xi (\omega; k), k \in \mathbb{N} \} $$
where for simplicity I'm thinking of a finished set $\Omega$, where the single elementary events are indicated with $ \omega$ and the random variables (functions only of $ \omega$ ) that form the random process are a countable set. So in my head I'm seeing this:
where, even if not drawn, obviously the domain of each $ \xi (\omega; k)$ is the whole $ \Omega$. If I have not yet said stupid things, it means that when you try the experiment a single time, the number that each of the $ \xi (\omega; k)$ is given.
So I ask myself: how is thermal noise schematized in this perspective? Who are the elementary events $ \omega$? All the values (e.g. voltage, in volts) that noise can assume? And if so, who are the various $ \xi (\omega; k)$, and how do they map the various $ \omega$ into $\mathbb{R}$?
Have mercy if my questions are stupid, but I have never approached these things until these days. Thanks in advance.