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La convergence en loi pour les processus à valeurs dans un espace nucléaire. (French) Zbl 0545.60012
We give a simple condition for compactness of a sequence of probability measures on C([0,\(\infty),E')\) or D([0,\(\infty),E')\) where E is a nuclear space \((D({\mathbb{R}}^ d)\) for instance). This extends a result obtained by I. Mitoma [Ann. Probab. 11, 989-999 (1983; Zbl 0527.60004)] for \(E={\mathcal S}({\mathbb{R}}^ d)\).

MSC:
60B10 Convergence of probability measures
60B11 Probability theory on linear topological spaces
60G20 Generalized stochastic processes
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