I understand the question as being motivated by a plan to embark on original research at the interface of ergodic theory and stochastic analysis. For such a purpose it seems helpful if the topic is less mature, less well established, and perhaps less well covered by "landmark papers".

<A HREF="https://en.wikipedia.org/wiki/Ergodicity_economics">Ergodicity economics</A> is a branch of mathematical finance at this interface. A foundational paper is by <A HREF="https://www.nature.com/articles/s41567-019-0732-0">Ole Peters</A> (2019). <A HREF="https://scholar.google.com/scholar?cites=16380731883124301371&as_sdt=2005&sciodt=0,5&hl=en">Google Scholar</A> can point you to an extensive literature.