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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 대한수학회 대한수학회보 대한수학회보 제58권 제6호
- 발행연도
- 2021.11
- 수록면
- 1,419 - 1,443 (25page)
- DOI
- 10.4134/BKMS.b200980
이용수
초록· 키워드
오류제보하기
The asymmetric Laplace distribution arises as a limiting distribution of geometric summations of independent and identically distributed random variables with finite second moments. The main purpose of this paper is to study the weak limit theorems for geometric summations of independent (not necessarily identically distributed) random variables together with convergence rates to asymmetric Laplace distributions. Using Trotter-operator method, the orders of approximations of the distributions of geometric summations by the asymmetric Laplace distributions are established in term of the ``large--$\mathcal{O}$" and ``small--o" approximation estimates. The obtained results are extensions of some known ones.
목차
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참고문헌 (28)
참고문헌 신청
J. Blanchet / 2007 / Uniform renewal theory with applications to expansions of random geometric sums / Adv. in Appl. Probab 39(4):1070~1097
P.L. Butzer / 1978 / General theorems on rates of convergence in distribution of random variables I. General limit theorems / Journal of Multivariate Analysis 8(2):181~201
P.L. Butzer / 1978 / General theorems on rates of convergence in distribution of random variables II. Applications to the stable limit laws and weak law of large numbers / Journal of Multivariate Analysis 8(2):202~221
P.L Butzer / 1975 / On the rate of approximation in the central limit theorem / Journal of Approximation Theory 13(3):327~340
C. D¨obler / 2015 / New Berry-Esseen and Wasserstein bounds in the CLT for non-randomly centered random sums by probabilistic methods / ALEA Lat. Am. J. Probab. Math. Stat 12(2):863~902
P.L. Butzer / 1978 / General theorems on rates of convergence in distribution of random variables II. Applications to the stable limit laws and weak law of large numbers / Journal of Multivariate Analysis 8(2):202~221
P.L Butzer / 1975 / On the rate of approximation in the central limit theorem / Journal of Approximation Theory 13(3):327~340
C. D¨obler / 2015 / New Berry-Esseen and Wasserstein bounds in the CLT for non-randomly centered random sums by probabilistic methods / ALEA Lat. Am. J. Probab. Math. Stat 12(2):863~902
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