LIMSUP RESULTS AND A GENERALIZED UNIFORM LIL FOR AN LPQD SEQUENCE Choi, Yong-Kab; Hwang, Kyo-Shin; Moon, Hee-Jin;
In this paper we establish some limsup results and a generalized uniform law of the iterated logarithm (LIL) for the increments of partial sums of a strictly stationary and linearly positive quadrant dependent (LPQD) sequence of random variables.
linearly positive quadrant dependence;strictly stationary sequence;law of the iterated logarithm;
Classification of bi-qutrit positive partial transpose entangled edge states by their ranks, Journal of Mathematical Physics, 2012, 53, 5, 052201
Y. K. Choi, Limsup results and a uniform LIL for partial sums of an LNQD sequence, Appl. Math. Lett. 24 (2011), no. 2, 138-144.
Y. K. Choi and M. Csorgo, Limsup results and LIL for partial sum processes of a Gaussian random eld, Acta Math. Sinica. 24 (2008), no. 9, 1497-1506.
Y. K. Choi, K. S. Hwang, T. S. Kim, Z. Y. Lin, and W. S. Wang, Asymptotic behaviors for partial sum processes of a Gaussian sequence, Acta Math. Hungar. 103 (2004), no. 1-2, 43-54.
J. Esary, F. Proschan, and D. Walkup, Association of random variables with applications, Ann. Math. Statist. 38 (1967), no. 4, 1466-1474.
E. L. Lehmann, Some concepts of dependence, Ann. Math. Statist. 37 (1966), no. 4, 1137-1153.
Y. X. Li and J. F. Wang, The law of the iterated logarithm for positively dependent random variables, J. Math. Anal. Appl. 339 (2008), no. 1, 259-265.
C. M. Newman, Asymptotic independence and limit theorems for positively and negatively dependent random variables, Inequalities in statistics and probability (Lincoln, Neb., 1982), 127-140, IMS Lecture Notes Monogr. Ser., 5, Inst. Math. Statist., Hayward, CA, 1984.
Y. Yang and Y. B. Wang, The asymptotical normality of the renewal process generated by strictly stationary LPQD sequences, Chinese J. Appl. Probab. Statist. 24 (2008), no. 1, 37-42.