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XIII: 24, 260-280, LNM 721 (1979)
ÉMERY, Michel
Une topologie sur l'espace des semimartingales (General theory of processes, Stochastic calculus)
The stability theory for stochastic differential equations was developed independently by Émery (Zeit. für W-Theorie, 41, 1978) and Protter (same journal, 44, 1978). However, these results were stated in the language of convergent subsequences instead of true topological results. Here a linear topology (like convergence in probability: metrizable, complete, not locally convex) is defined on the space of semimartingales. Side results concern the Banach spaces $H^p$ and $S^p$ of semimartingales. Several useful continuity properties are proved
Comment: This topology has become a standard tool. For its main application, see the next paper 1325
Keywords: Semimartingales, Spaces of semimartingales
Nature: Original
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