The three operators theorem. (Le théorème des trois opérateurs.) (French) Zbl 0909.60036

The author proves the following main results: Let \(E,F,G,H\) be Banach spaces, \(F\) is reflexive and separable, \(G\) is reflexive; \(u:E\to F\), and \(v:F\to G\) are linear continuous functions “0-radonifiante”, \(w:G\to H\) is 1-summable. If \(L\) is a cylindrical semi-martingale with values in \(E\), \(L\in {\mathcal L} (E';{\mathcal S} {\mathcal M})\) is a local semi-martingale with values in \(H\). If \(L\) is a semi-martingale with values in \(H\) and satisfies the Radon-Nikodym properties (in particular is reflexive), then \(wvu(L) \in{\mathcal S} {\mathcal M} (H)\).


60G44 Martingales with continuous parameter
60B05 Probability measures on topological spaces
Full Text: DOI Numdam EuDML


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