# Is it possible to define a mixed normal having conditional variance almost everywhere null?

I'm trying to proving the stable limit of a martingale M_n(t). When I calculate the limit in probability of its quadratic variation, I find that it is always null except for a point.

It seems to me that the classical hypotheses necessary to prove the stable convergence of the limit towards a mixing normal drop down.

Does somebody know some references that could help me to figure this problems out? What kind of limit process should I expect to find?

Thank you for any kind of suggestions!!!

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