XVI: 27, 314-318, LNM 920 (1982)
LENGLART, Érik
Sur le théorème de la convergence dominée (
General theory of processes,
Stochastic calculus)
Consider previsible processes $U^n,U$ such that $U^n_T\rightarrow U_T$ in some sense at bounded previsible times $T$. The problem discussed is whether stochastic integrals $\int U^n_s dX_s$ converge (in the same sense) to $\int U_sdX_s$. Under a domination hypothesis, the answer is shown to be positive if the convergence is either weak convergence in $L^1$, or convergence in probability. The existence of the limiting process $U$ is not assumed in the paper; it is proved by a modification of an argument of Mokobodzki for which see
1110Keywords: Stopping times,
Optional processes,
Weak convergence,
Stochastic integralsNature: Original
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