I have a follow up question from my previous question on math.SE, where I asked about the First use of little $o$ notation - for those who want to check - the answer goes back to Landau ($1909$), this could really be one of the earliest occurrences (the definition is motivated by the big $O$ notation and there is no reference to any other work, so it seems genuin).

Now I wonder when the slightly different notation of $o_p(\cdot)$ notation was first introduced. Clearly later but unfortunately there is no historically reference on Wikipedia. Does anyone have a clue or reference where I should look into?


1 Answer 1


From Earliest use of mathematical symbols:

The convergence in probability symbol plim was introduced by H. B. Mann and A. Wald "On Stochastic Limit and Order Relationships," Annals of Mathematical Statistics, 14, (1943), 217-226. The stochastic order symbols $O_p$ and $o_p$, modelled on the $O$ and $o$, or Landau symbols, were introduced in the same paper.


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