Authors: and
View More View Less
• | 2 Hungarian Academy of Sciences Alfréd Rényi Institute of Mathematics HU–1364 Budapest
Restricted access

USD  \$25.00

### 1 year subscription (Individual Only)

USD  \$800.00

Let us consider a triangular array of random vectors (X (n) j; Y (n) j), n = 1;2;: : :, 1 5 j 5 kn, such that the first coordinates X (n) j take their values in a non-compact Lie group and the second coordinates Y (n) j in a compact group. Let the random vectors (X (n) j; Y (n) j) be independent for fixed n, but we do not assume any (independence type) condition about the relation between the components of these vectors. We show under fairly general conditions that if both random products Sn = kn Q j=1 X (n) j and Tn = kn Q j=1 Y (n) j have a limit distribution, then also the random vectors (Sn; Tn) converge in distribution as n !1 . Moreover, the non-compact and compact coordinates of a random vector with this limit distribution are independent.

• BILLINGSLEY, P., Convergence of probability measures, John Wiley & Sons, Inc., New York-London-Sidney-Toronto, 1968. MR38 #1718

Convergence of probability measures , ().

• RAUGI, A., Théorème de la limite centrale pour un produit semi-direct d'un groupe de Lie résoluble simplement connexe de type rigide par un groupe compact, Probability measures on groups (Proc. Fifth Conf., Oberwolfach, 1978), ed. by H. Heyer, Lecture Notes in Math., 706, Springer, Berlin-Heidelberg-New York, 1979, 257-324. MR83c:60015

Théorème de la limite centrale pour un produit semi-direct d'un groupe de Lie résoluble simplement connexe de type rigide par un groupe compact , () 257 -324.

• STROMBERG, K., Probabilities on a compact group, Trans. Amer. Math. Soc.94 (1960), 295-309. MR22 #5692

'Probabilities on a compact group ' () 94 Trans. Amer. Math. Soc. : 295 -309.

• WEHN, D., Probabilities on Lie groups, Proc. Nat. Acad. Sci. U.S.A.48 (1962), 791-795. MR27 #3011

'Probabilities on Lie groups ' () 48 Proc. Nat. Acad. Sci. U.S.A. : 791 -795.

• HEYER, H. and PAP, G., Convergence of noncommutative triangular arrays of probability measures on a Lie group, J. Theoret. Probab.10 (1997), 1003-1052. MR2000b:60012

'Convergence of noncommutative triangular arrays of probability measures on a Lie group ' () 10 J. Theoret. Probab. : 1003 -1052.

• MAJOR, P., The limit behavior of elementary symmetric polynomials of i.i.d. random variables when their order tends to infinity, Ann. Probab.27 (1999), 1980-2010.

'The limit behavior of elementary symmetric polynomials of i.i.d. random variables when their order tends to infinity ' () 27 Ann. Probab. : 1980 -2010.

• PAP, G., Central limit theorems on nilpotent Lie groups, Probab. Math. Statist.14 (1993), 287-312. MR96c:22010

'Central limit theorems on nilpotent Lie groups ' () 14 Probab. Math. Statist. : 287 -312.

• PAP, G., Lindeberg-Feller theorems on Lie groups, Arch. Math.72 (1999), 328-336.

'Lindeberg-Feller theorems on Lie groups ' () 72 Arch. Math. : 328 -336.

All Time Past Year Past 30 Days
Abstract Views 8 8 1
Full Text Views 5 1 0