I have seen both statements being used frequently in formal texts (i.e. lecture notes), i.e. "adopted" as well as "adapted" when referring to a process that is "adapted" to some filtration.
Which one is correct? For years now, I keep thinking that "adopted" is in fact miss-spelling of "adapted", because in the English language, it does not make sense to me to say that a process is "adopted" to filtration (could be "adopted by filtration", but it seems odd to say it is "adopted to filtration").
Are both acceptable?