H-K. Hwang, Large Deviations for Combinatorial Distributions I: Central Limit Theorems, Annals of Applied Probability, 6, 297-319, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... deviations of combinatorial distributions II: Local limit theorems Academia Sinica, Taipei June 6, 1997 1 Main result This paper is a sequel to our paper [17] where we derived a general central limit theorem for probabilities of large deviations applicable to many classes of combinatorial structures and arithmetic functions; we consider corresponding local limit theorems in this paper. More precisely, given a sequence of integral random variables n ....

....O(oe n ) Our interest here is not to derive asymptotic expression for n = mg valid for the widest possible range of m, but to show that for m lying in the interval n Sigma O(oe n ) very precise asymptotic formulae can be obtained. These formulae are in close connection with our results in [17]. Although local limit theorems receive a constant research interest [2, 3, 7, 14, 13, 24] our approach and results, especially Theorem 1, seem rarely discussed in a systematic manner. Recall that a lattice random variable X is said to be of maximal span h if X takes only values of the form b ....

[Article contains additional citation context not shown here]

H.-K. Hwang, Large deviations of combinatorial distributions I: central limit theorems, 6, 297-- 319 (1996).

.... deviations of combinatorial distributions II: Local limit theorems Academia Sinica, Taipei June 6, 1997 1 Main result This paper is a sequel to our paper [17] where we derived a general central limit theorem for probabilities of large deviations applicable to many classes of combinatorial structures and arithmetic functions; we consider corresponding local limit theorems in this paper. More precisely, given a sequence of integral random variables ....

....to O(# n ) Our interest here is not to derive asymptotic expression for n = m valid for the widest possible range of m, but to show that for m lying in the interval n O(# n ) very precise asymptotic formulae can be obtained. These formulae are in close connection with our results in [17]. Although local limit theorems receive a constant research interest [2, 3, 7, 14, 13, 24] our approach and results, especially Theorem 1, seem rarely discussed in a systematic manner. Recall that a lattice random variable X is said to be of maximal span h if X takes only values of the form b ....

[Article contains additional citation context not shown here]

H.-K. Hwang, Large deviations of combinatorial distributions I: central limit theorems, 6, 297-- 319 (1996).

....= a ln( am(1 z a ) az a (am 1) 1 z a ) az a ) ln z a (30) 2 a = a(1 a) a 2 z a ( m 2 z a a amz a 2mz 2z am 2 am 2m) az a ( m mz a z a ) 31) a = log[ a (1 z a ) P(H)z m a ] 32) Our proof is purely analytical. A detailed description of this method [JR86, FS93, Hwa96, Hwa98, RS97] that is now classical, can be found in [FS93] Cauchy formula for univariate series rewrites: P 1;n (u 1 ) 1 2i I T (z; u 1 ; 1) z n 1 dz : 33) It follows from Proposition 2.3 that, for any given u 1 = e t around 1, generating function T (z; u 1 ; 1) has a unique pole ....

H. K. Hwang. Large Deviations of Combinatorial Distributions I: Central Limit Theorems. Annals of Applied Probability, 6(1):297-319, 1996.

....Second, our methods obtain automatically a full asymptotic expansion of a r1 ; r d in decreasing powers of the indices r j . This is certainly not inherent in the existing results, whose relatively short proofs involve inversion of the characteristic function (see however Hwang (1995) and Hwang (1996) for something in this direction) The expansion to n terms is completely e ective in terms of the rst n partial derivatives of 1=F at z, as is the error bound. Third, these results explicitly cover the case where the pole at z has order greater than 1. The behavior in this case is not according ....

Hwang, H.-K. (1996), `Large deviations for combinatorial distributions. I. Central limit theorems', Ann. Appl. Probab.

....Second, our methods obtain automatically a full asymptotic expansion of a r1 ; r d in decreasing powers of the indices r j . This is certainly not inherent in the existing results, whose relatively short proofs involve inversion of the characteristic function (see however Hwang (1995) and Hwang (1996) for something in this direction) The expansion to n terms is completely e ective in terms of the rst n partial derivatives of 1=F at z, as is the error bound. ASYMPTOTICS OF MULTIVARIATE SEQUENCES I 5 Third, these results explicitly cover the case where the pole at z has order greater than 1. ....

Hwang, H.-K. (1996), `Large deviations for combinatorial distributions. I. Central limit theorems', Ann. Appl. Probab. 6(1), 297-319.

No context found.

H-K. Hwang, Large Deviations for Combinatorial Distributions I: Central Limit Theorems, Annals of Applied Probability, 6, 297-319, 1996.

No context found.

H.-K. Hwang. Large deviations of combinatorial distributions I: central limit theorems. Annals of Applied Probability, 6 (1996), 297--319.

No context found.

H.-K. Hwang. Large deviations of combinatorial distributions I: central limit theorems. submitted, 1994.

No context found.

H-K. Hwang, Large Deviations for Combinatorial Distributions I: Central Limit Theorems, Ann. Appl. Probab., 6, 297-319, 1996. 49

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC