Is there a concept similar to "continuous compounding" but related to dollar cost averaging when buying (e.g.) shares or bitcoins?

I know that dollar cost averaging (DCA) is "drip feeding" a total amount to be invested over regular intervals like daily, weekly or monthly, so that each share purchase (or whatever the investment is) is at the market rate at the time.

Is there a concept similar to continuous compounding, but related to DCA? as in, the "theoretical" effect of continuously streaming in (with infinitely small intervals) parts of the total sum to be invested?

I am taking continuous compounding to mean the theoretical maximum limit of compound interest, where daily interest compounds more quickly than monthly etc, and c.c. is "what would happen if interest was ‘streamed’ in infinitely small intervals".

(Assume there are no fees on any of the transactions, or the fee is a fixed % of the transaction size)

Have tried searching but either this info isn’t out there (or the concept doesn’t exist), or my search terms were just rubbish!

Edited to add what I am trying to achieve – I don’t think this will change my investment strategy, but I would like to understand "theoretically" if a concept similar to c.c. applies to dollar cost averaging, in terms of whether it’s meaningful to think about what would happen when "drip feeding" money in over smaller and smaller intervals. If so what is the name of this concept, if not then why does it not apply?

For example if I wanted to feed in that investment over 6 months. I’d "capture" the market price only 6 times if I invested monthly, 26 times if investing weekly, 182 times if investing daily, etc. It seems intuitive to me that the smaller the time interval, the closer the ‘accumulated’ purchase price tracks the actual market (and in the theoretical ‘continuous investment’ case, that it would track market prices exactly), but I can’t quite translate that in my head into what the actual effect is of "tracking the market price" by buying in smaller intervals.