What are the elements of a filtration generated by a Wiener process? I understand the concept of filtration intuitively, and I can wrtite down the elements of a filtration for example in the case of a coin toss game, but what are the sets in the filtration of a Wiener process at a given time? How do they look like?

For example, a stock price $S_t$ is usually modelled by the following
$$dS_t=S_tdt+S_tdW_t$$
where $W_t$ is a Wiener process. In this context, roughly speaking, events that generate the filtration (natural filtration of $W_t$) are any random events that can influence the stock price $S_t$. For instance, at time $t$ there is an earthquake at California that destroyed a factory of Tesla (event that consists of one outcome). $W_t$ goes down and, consequently, stock price falls. However, no-one knows all the random events that can happen at time $t$. You can only observe the stock price. Therefore, it is usually assumed that the natural filtration of a Wiener process is an abstract flow of information that is known up to time $t$.
