stochastic process

a stochastic process is a sequence of random variables whose index has the interpretation of time.
https://en.wikipedia.org/wiki/Stochastic_process

in the following, let $\text{[math]}$ be a polish space with borel $\text{[math]}$ -algebra $\text{[math]}$ . further, let $\text{[math]}$ be a probability space and let $\text{[math]}$ be arbitrary. we are mostly interested in the cases $\text{[math]}$ and $\text{[math]}$ an interval.

let $\text{[math]}$ . a family of random variables $\text{[math]}$ (on $\text{[math]}$ ) with values in $\text{[math]}$ is called a stochastic process with index set (or time set) $\text{[math]}$ and range $\text{[math]}$ .
[cite:;taken from @klenke_prob_2020 definition 9.1 (stochastic process)]

[cite:;taken from @klenke_prob_2020 chapter 9.1 processes, filtrations, stopping times]