Maximal inequalities for partial sums of independent random vectors with multi dimensional time parameters

Bibliography

• Breiman , L. 1968 . Probability , New York : Addison Wesley .
   Google Scholar
• Cairoli , R. Une ineqalite pour martingales a indices multiples et ses applications . Seminare de probabilites IV . pp. 1 – 27 . Berlin : Springer-Verlag . Lecture Notes in Mathematics
   Google Scholar
• De Acosta , A. and Samur , J.D. 1979 . Infinitely divisible probability measures and the converse Kolmogorov inequality in Banach spaces . Studia Mathematica , T. LXVI : 143 – 160 .
   Google Scholar
• Dozzi , M. 1989 . “ Stochastic Processes with a multidimensional parameter ” . In Pitman Research Notes in Mathematics Series , Longman Scientific & Technical .
   Google Scholar
• Etemadi , N. 1984 . On the maximal inequality for the average of pairwise i.i.d. random variables . Commun. Statist.-Theor. Meth , 13 ( 22 ) : 2749 – 2756 .
   Web of Science ®Google Scholar
• Etemadi , N. 1985 . On some classical results in probability theory . Sankhya Series A , 47 ( 2 ) : 215 – 221 .
   Google Scholar
• Etemadi , N. 1990 . A simple inequality for independent random vectors . Sankhya , 47 ( 2 ) Preprint. To appear in
   Google Scholar
• Klesov , O.I. 1982 . On the law of iterated logarithm . Theory Prob. Math. Statist , 27 ( 2 ) : 60 – 67 .
   Google Scholar
• Loeve , M. 1963 . Probability Theory , New York : Lan Nostrand Company .
   Google Scholar
• Paranjape , S.R. and Park , C. 1973 . Laws of iterated logarithm of multi-parameter Wiener Processes . J. Multivariate Analysis , 3 : 132 – 136 .
   Google Scholar
• Pyke , R. , Kendall and Harding . 1973 . Stochastic analysis , London : John Wiley & Sons . New York-Sydney
   Google Scholar
• Smythe , R. 1973 . Strong laws of large numbers for r-dimensional arrays of random variables . Ann. Probability , 1 : 164 – 170 .
   Web of Science ®Google Scholar
• Smythe , R. 1974 . Sums of inependent random variables on partially ordered sets . Ann. Probability , 2 ( 5 ) : 906 – 917 .
   Web of Science ®Google Scholar
• Walsh , T.B. 1986 . Martingales with a Multidimensional parameter and Stochastic Integrals in the Plane , 1215 ( 5 ) : 329 – 491 . Lecture Notes in Math
   Google Scholar
• Wichura , M.J. 1969 . Inequalities with applications to weak convergence of random processes with multidimensional time parameters . Ann. Math. Stat , 40 ( 5 ) : 681 – 687 .
   Google Scholar