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3 matches found
III: 08, 143-143, LNM 88 (1969)
MEYER, Paul-André
Un lemme de théorie des martingales (Martingale theory)
The author apparently believed that this classical and useful remark was new (it is often called ``Hunt's lemma'', see Hunt, Martingales et Processus de Markov, Masson 1966, p.47)
Keywords: Almost sure convergence
Nature: Well-known
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IV: 01, 1-27, LNM 124 (1970)
Une inégalité pour martingales à indices multiples et ses applications (Several parameter processes)
This paper was the starting point of the theory of two-parameter martingales. It proves the corresponding Doob inequality and convergence theorem, with an application to biharmonic functions
Comment: The next landmark in the theory is Cairoli-Walsh, Acta. Math., 134, 1975. For the modern results, see Imkeller, Two Parameter Processes and their Quadratic Variation, Lect. Notes in M. 1308, 1989
Keywords: Two-parameter martingales, Maximal inequality, Almost sure convergence
Nature: Original
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XIII: 13, 162-173, LNM 721 (1979)
Sur la convergence des martingales indexées par ${\bf N}\times{\bf N}$ (Several parameter processes)
For two parameter (discrete) martingales, it is known that uniform integrability does not imply a.s. convergence. But if all (discrete) martingale transforms by indicators of previsible sets are uniformly integrable, then a.s. convergence obtains
Keywords: Almost sure convergence, Martingale transforms
Nature: Original
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