DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Choi, Bong-Dae | - |
dc.contributor.advisor | 최봉대 | - |
dc.contributor.author | Sung, Soo-Hak | - |
dc.contributor.author | 성수학 | - |
dc.date.accessioned | 2011-12-14T04:57:42Z | - |
dc.date.available | 2011-12-14T04:57:42Z | - |
dc.date.issued | 1985 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=64429&flag=dissertation | - |
dc.identifier.uri | http://hdl.handle.net/10203/42277 | - |
dc.description | 학위논문(석사) - 한국과학기술원 : 응용수학과, 1985.2, [ [ii], 26 p. ; ] | - |
dc.description.abstract | Let ($X_n$) be a sequence of random variables and $S_n = \sum^n_{i=1}X_i$. Pyke and Root (1968) proved that if ($X_n$) is a sequence of i.i.d. random variables with $E│X_1│^r<∞$, then ($S_n-ES_n)/n^{1/r} → 0 a.s. and in $L^r$, 1≤r<2. Chatterji(1969) extended this result to the case where the $X_n``s$ are dominated in distribution by a random variable X with $E│X│^r<∞$. Recently Etemadi(1981, 1983) proved that Pyke and Root``s result under the weaker condition of pairwise independence when r=1. In this thesis, we prove that if ($X_n$) are uncorrelated and their second moments have a common bound, then ($S_n-ES_n)/n^{1/r} → 0 a.s. for 1≤r<2. We also prove that if ($X_n$) are pairwise independent and dominated in distribution by a random variable X with $E(│X│^r(log^+│X│^r)^2)<∞$, then ($S_n-ES_n)/n^{1/r} → 0 a.s. for $1<r<2$. Finally, we prove that if ($X_n$) are pairwise independent and dominated in distribution by a random variable X with $E│X│^r<∞, then $(S_n-ES_n)/n^{1/r}$ → 0 in $L^1$ for 1≤r<2$. | eng |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.title | On convergence of normalized partial sums | - |
dc.title.alternative | 정규화한 부분합의 수렴성에 관한 연구 | - |
dc.type | Thesis(Master) | - |
dc.identifier.CNRN | 64429/325007 | - |
dc.description.department | 한국과학기술원 : 응용수학과, | - |
dc.identifier.uid | 000831194 | - |
dc.contributor.localauthor | Choi, Bong-Dae | - |
dc.contributor.localauthor | 최봉대 | - |
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