Nguyen-Minh-Duc; Nguyen-Xuan-Loc On the transformation of martingales with a two dimensional parameter set by convex functions. (English) Zbl 0558.60042 Z. Wahrscheinlichkeitstheor. Verw. Geb. 66, 19-24 (1984). This paper partially answers a P. A. Meyer’s question: if M is a two- indices martingale and f is a convex function, is f(M) always a martingale? Reducing the problem to the one-dimensional case, it is given as a sufficient condition when M is strong and bounded in a convenient sense that f” is convex too. Reviewer: B.Prum MSC: 60G60 Random fields 60G44 Martingales with continuous parameter 60H05 Stochastic integrals Keywords:two dimensional martingale; Ito formula PDFBibTeX XMLCite \textit{Nguyen-Minh-Duc} and \textit{Nguyen-Xuan-Loc}, Z. Wahrscheinlichkeitstheor. Verw. Geb. 66, 19--24 (1984; Zbl 0558.60042) Full Text: DOI References: [1] Cairoli, R.; Walsh, J. R., Stochastic integrals in the plane, Acta Math., 134, 111-183 (1975) · Zbl 0334.60026 · doi:10.1007/BF02392100 [2] Guyon, X.; Prum, B., Semi-martingales à indice dans R^2, Thèse de Doctorat d’Etat (1980), Orsay: Univ. Paris-Sud, Orsay · Zbl 0447.60041 [3] Guyon, X., Deux résultats sur les martingales browniennes à deux indices, C.R. Acad. Sci. Paris, sér. 1, 295, 359-361 (1982) · Zbl 0499.60054 [4] Meyer, P. A., Théorie élémentaire des processus à deux indices (1981), Berlin-Heidelberg-New York: Springer, Berlin-Heidelberg-New York · Zbl 0461.60072 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.