XVI: 24, 268-284, LNM 920 (1982)
UPPMAN, Are
Sur le flot d'une équation différentielle stochastique (Stochastic calculus)
This paper is a companion to 1506, devoted to the main results on the flow of a (Lipschitz) stochastic differential equation driven by continous semimartingales: non-confluence of solutions from different initial points, surjectivity of the mapping, smooth dependence on the initial conditions. The proofs have been greatly simplified
Keywords: Stochastic differential equations, Flow of a s.d.e., Injectivity
Nature: Exposition, Original additions
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XVI: 25, 285-297, LNM 920 (1982)
UPPMAN, Are
Un théorème de Helly pour les surmartingales fortes (Martingale theory)
Provide the set of (optional) strong supermartingales $X$ of the class (D) with the topology of weak $L^1$--convergence of $X_T$ at each stopping time $T$. Then it is shown that any subset which belongs uniformly to the class (D) is relatively compact, also in the sequential sense of extracting convergent subsequences
Comment: This paper was suggested by a similar result of Mokobodzki for strongly supermedian functions in potential theory
Keywords: Supermartingales, Strong supermartingales
Nature: Original
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