Article PDF
References
Cairoli, R.: Une inegalité pour martingales à indices multiples et ses applications. Seminaire de Probabilités IV. Lecture Notes in Mathematics 124, 1–28. Berlin-Heidelberg-New York: Springer 1970
Cairoli, R., Walsh, J.B.: Stochastic integrals in the plane. Acta Math. 134, 111–183 (1975)
Dieudonné, J.: Sur un théorème de Jessen. Fundamenta Math. 37, 242–248 (1950)
Dubins, L.E., Savage, L.J.: How to Gamble if You Must: Inequalities for Stochastic Processes. New York: McGraw-Hill 1965
Dubins, L.E., Pitman, J.W.: A pointwise ergodic theorem for the group of rational rotations. Trans. Amer. Math. Soc. 251, 299–307 (1979)
Dubins, L.E., Pitman, J.W.: A divergent, two-parameter, bounded martingale. [To appear in Proc. Amer. Math. Soc. 1980]
Gut, A.: Convergence of reversed martingales with multidimensional indices. Duke Math. J. 43, 2, 269–275 (1976)
Krickeberg, K.: Convergence of martingales with a directed index set. Trans. Amer. Math. Soc. 83, 313–337 (1956)
Lai, T.L., Robbins, H.: Maximally dependent random variables. Proc. Nat. Acad. Sci. U.S.A. 73, 2, 286–288 (1976)
Lai, T.L., Robbins, H.: A class of dependent random variables and their maxima. Z. Wahrscheinlichkeitstheorie verw. Gebiete 42, 89–111 (1978)
Mallows, C.L.: Extrema of expectations of uniform order statistics. SIAM Review 11, 410–411 (1969)
Neveu, J.: Discrete Parameter Martingales. Amsterdam: North-Holland 1975; New York: American Elsevier 1975
Smythe, R.T.: Sums of independent random variables on partially ordered sets. Ann. Probability 2, 5, 906–917 (1974)
Tchen, A.: Inequalities for distributions with given marginals. Stanford University Technical Report (1976)
Author information
Authors and Affiliations
Additional information
Research supported by National Science Foundation Grant MCS 7701665
Research supported by National Science Foundation Grant MCS 7510376
Rights and permissions
About this article
Cite this article
Dubins, L.E., Pitman, J. A maximal inequality for skew fields. Z. Wahrscheinlichkeitstheorie verw Gebiete 52, 219–227 (1980). https://doi.org/10.1007/BF00538887
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00538887