Can we say this?

As N gets uniformly larger then Ito's conditions uniformly go to Newton's conditions?

I don;t think so, Ito has stopping points, Gibbs states.  They are the quantum contradictions.  The system holds at a state where the cost of re-quantization is larger than he gain.  Minsky uncertainty wells.

But within a region about these points, Newton holds to a point that we can net present value a sub-graph, use some universal time standard,imprecisely. The shop owner can do calculus with the mean value of his inventory. He can, effectively, pick a single unit, the shop is optimally full, call that one unit of break even, including profit, and note the integration limits.  That matches his net present value to a uniform X axis on a yield curve.

In the  queuing model, using newton estimates means assuming gaussian inter-arrival times, so you can use arrival rate referenced to time as an integrating variable.  But, beneath the surface are finite monte carlo sequences, constructed of mostly ordered generators...