Large deviations of combinatorial distributions II. Local limit theorems

被引：0

作者：

Hwang, HK ^{[1
]}

机构：

[1] Acad Sinica, Inst Stat Sci, Taipei 115, Taiwan

来源：

ANNALS OF APPLIED PROBABILITY | 1998年 / 8卷 / 01期

关键词：

large deviations; local limit theorems; asymptotic expansion; saddlepoint method; combinatorial schemes; singularity analysis; additive arithmetical functions;

D O I：

暂无

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We derive a general local limit theorem for probabilities of large deviations for a sequence of random variables by means of the saddlepoint method on Laplace-type integrals. This result is applicable to parameters in a number of combinatorial structures and the distribution of additive arithmetical functions.

引用

页码：163 / 181

页数：19

共 30 条

[1] [Anonymous], 1990, MATH ANAL ALGORITHMS
[2] [Anonymous], INTRO THEORIE ANAL P
[3] [Anonymous], 1973, J COMB THEORY A
[4] TOTAL VARIATION ASYMPTOTICS FOR POISSON-PROCESS APPROXIMATIONS OF LOGARITHMIC COMBINATORIAL ASSEMBLIES
ARRATIA, R
STARK, D
TAVARE, S
[J]. ANNALS OF PROBABILITY, 1995, 23 (03) : 1347 - 1388
[5] CANFIELD ER, 1977, J COMB THEORY A, V23, P275
[6] LARGE DEVIATION LOCAL LIMIT-THEOREMS FOR ARBITRARY SEQUENCES OF RANDOM-VARIABLES
CHAGANTY, NR
SETHURAMAN, J
[J]. ANNALS OF PROBABILITY, 1985, 13 (01) : 97 - 114
[7] Comtet L., 1974, ADV COMBINATORICS AR
[8] CRAMER H., 1937, Cambridge tracts in mathematics and mathematical physics, V36
[9] A BIVARIATE ASYMPTOTIC-EXPANSION OF COEFFICIENTS OF POWERS OF GENERATING-FUNCTIONS
DRMOTA, M
[J]. EUROPEAN JOURNAL OF COMBINATORICS, 1994, 15 (02) : 139 - 152
[10] ON THE INTEGERS HAVING EXACTLY K PRIME FACTORS
ERDOS, P
[J]. ANNALS OF MATHEMATICS, 1948, 49 (01) : 53 - 66

← 1 2 3 →