3 ms·
I think this article is not "martingales for laypeople". It is "martingales for math nerds" where the application is solving certain types of math problems to
by throwaway81523 4y ago
I think this article is not "martingales for laypeople". It is "martingales for math nerds" where the application is solving certain types of math problems to mathematical standards of rigor. For that rigor, you do need the sigma algebras. I would say also, the target reader of the article already knows what a sigma algebra is, so the formal definition is given only for review purposes, plus to motivate something the author does about finding a disjoing minimal cover of the sample space. I haven't yet read the article carefully enough to understand why he does that.
- synergy7 4y agoI think the author uses minimal set because it allows constructing any sigma-algebra from it. This (minimal set-based construction) is only possible for finite spaces. It allows, for example, an intuitive explanation of how sigma algebra F2 is coarser than F1. It serves a similar purpose as Borel sigma algebras in the general case, although a minimal set does not need to be a sigma algebra. Using different sigma algebras allows describing easily all events on which the probability is defined, and how those events may change with time (filtration). I am not sure how use of sigma algebras (or algebras for finite case) can be avoided in general.