XV: 37, 547-560, LNM 850 (1981)
JACOD, Jean
Convergence en loi de semimartingales et variation quadratique (
General theory of processes,
Stochastic calculus)
The convergence in law of cadlag processes to a cadlag process being understood in the sense of Skorohod, the problem is to find sufficient conditions under which, given semimartingales $X^n$ and $X$ such that $X^n\rightarrow X$ in law, one may deduce that $[X^n,X^n]$ converges in law to $[X,X]$. This is achieved assuming a uniform bound on the expectations of the supremum of the jumps. A version of the theorem applied to processes which are not semimartingales, but are equal to semimartingales on large sets
Keywords: Semimartingales,
Skorohod topology,
Convergence in lawNature: Original
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