IV: 01, 1-27, LNM 124 (1970)
CAIROLI, Renzo
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 convergenceNature: Original
Retrieve article from Numdam
