Kartashova, S. S. A generalization of Garsia’s inequality to two-parameter supermartingales. (English. Ukrainian original) Zbl 0842.60043 Theory Probab. Math. Stat. 48, 13-18 (1994); translation from Teor. Jmovirn. Mat. Stat. 48, 19-27 (1993). Summary: The question is studied whether a generalization of the well-known Garsia inequality for supermartingales can be proved for two-dimensional potentials. The inequality obtained allows us to estimate moments of increasing fields generated by two-parameter potentials. A counterexample is given demonstrating that an exact analogue of Garsia’s inequality cannot be obtained in the plane. MSC: 60G48 Generalizations of martingales Keywords:supermartingales; two-parameter potentials; Garsia’s inequality PDFBibTeX XMLCite \textit{S. S. Kartashova}, Theory Probab. Math. Stat. 48, 1 (1993; Zbl 0842.60043); translation from Teor. Jmovirn. Mat. Stat. 48, 19--27 (1993)