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In page 137 of Ethier and Kurtz(1986 - Markov processes, convergence and characterization) one reads:

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I don't see how that follows, imagine that $\Delta >\delta$ so $q(X(\delta), X(\Delta \wedge \delta)) = 0$ and if (8.27) were true then

$$q^{2\beta}(X(\delta), X(0))\leq a_\beta q^\beta(X(\delta), X(0)) $$ and suffices to take $q(X(\delta), X(0)) > a_\beta$ to see that this inequality doe not hold. (Or am I making a mistake)

If there is indeed a typo here, then how would one proceed with the proof of the result (8.18)?

Here below are some of the objects that come into play:

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Please let me know if you need any further description.

Conrado Costa
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  • Please make your question self-contained (i.e. add the relevant definitions and all the stuff needed to understand what you are actually asking). – saz Oct 05 '16 at 16:00
  • Sure @saz is there anytthing missing? maybe you found something... – Conrado Costa Oct 06 '16 at 06:53

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