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Nov 28, 2022 at 7:25 comment added Alex Appel Theorem 6.5 in Ethier and Kurtz was exactly what I was looking for. Problem resolved.
Nov 28, 2022 at 7:24 vote accept Alex Appel
Nov 27, 2022 at 2:54 comment added Alex Appel Thanks, this was extremely helpful! Tightness+"there can only be one limit point because the generators converge" sufficed quite nicely for my purposes, and I've got a few helpful references to chew on now. All I'm missing at this point is how to go back from the infinitesimal generator of the limiting stochastic process (known) to the actual differential equation for the limiting stochastic process, to show the limiting differential equation is what I conjectured it to be.
Nov 26, 2022 at 23:50 history answered Thomas Kojar CC BY-SA 4.0