Newman, C. M.; Wright, A. L. Associated random variables and martingale inequalities. (English) Zbl 0465.60010 Z. Wahrscheinlichkeitstheor. Verw. Geb. 59, 361-371 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 8 ReviewsCited in 49 Documents MSC: 60B10 Convergence of probability measures 60G44 Martingales with continuous parameter 60J65 Brownian motion Keywords:submartingale inequalities; maximal inequality; two-parameter Wiener process PDF BibTeX XML Cite \textit{C. M. Newman} and \textit{A. L. Wright}, Z. Wahrscheinlichkeitstheor. Verw. Geb. 59, 361--371 (1982; Zbl 0465.60010) Full Text: DOI References: [1] Barlow, R., Proschan, F.: Statistical Theory of Reliability and Life Testing. New York: Holt, Rinehart and Winston 1975 · Zbl 0379.62080 [2] Billingsley, P.: Convergence of Probability Measure. New York: Wiley 1968 · Zbl 0172.21201 [3] Cairoli, R.: Une inégalité pour martingales à indices multiples et ses applications. Lecture Notes in Math. 124, 1-27. Berlin-Heidelberg-New York: Springer 1968 [4] Chung, K.L.: A Course in Probability Theory. New York: Academic Press 1974 · Zbl 0345.60003 [5] Esary, J., Proschan, F., Walkup, D.: Association of random variables with applications. Ann. Math. Statist. 38, 1466-1474 (1967) · Zbl 0183.21502 · doi:10.1214/aoms/1177698701 [6] Fortuin, C., Kastelyn, R., Ginibre, J.: Correlation inequalities on some partially ordered sets. Comm. Math. Phys. 22, 89-103 (1971) · Zbl 0346.06011 · doi:10.1007/BF01651330 [7] Garsia, A.: On a convex function inequality for submartingales. Ann. Probab. 1, 171-174 (1973) · Zbl 0289.60026 · doi:10.1214/aop/1176997032 [8] Harris, T.E.: A lower bound for the critical probability in a certain percolation process. Proc. Cambridge Philos. Soc. 59, 13-20 (1960) · Zbl 0122.36403 · doi:10.1017/S0305004100034241 [9] Lebowitz, J.: Bounds on the correlations and analyticity properties of ferromagnetic Ising spin systems. Comm. Math. Phys. 28, 313-321 (1972) · doi:10.1007/BF01645632 [10] Newman, C.: Normal fluctuations and the FKG inequalities. Comm. Math. Phys. 74, 119-128 (1980) · Zbl 0429.60096 · doi:10.1007/BF01197754 [11] Newman, C., Wright, A.: An invariance principle for certain dependent sequences. Ann. Probab. 9, 671-675 (1981) · Zbl 0465.60009 · doi:10.1214/aop/1176994374 [12] Pitman, J.W.: A note on L2 maximal inequalities. Séminaire de Probabilités XV. Lecture Notes in Math. Berlin-Heidelberg-New York: Springer 1981 [13] Straf, M.L.: Weak convergence of stochastic processes with several parameters. Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability 2, 187-221. Univ. Calif. 1972 · Zbl 0255.60019 [14] Wichura, M.: Inequalities with applications to the weak convergence of random processes with multi-dimensional time parameters. Ann. Math. Statist. 40, 681-687 (1969) · Zbl 0214.17701 · doi:10.1214/aoms/1177697741 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.