DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Choi, Bong-Dae | - |
dc.contributor.advisor | 최봉대 | - |
dc.contributor.author | Park, Kwang-Kyu | - |
dc.contributor.author | 박광규 | - |
dc.date.accessioned | 2011-12-14T04:57:58Z | - |
dc.date.available | 2011-12-14T04:57:58Z | - |
dc.date.issued | 1987 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=65547&flag=dissertation | - |
dc.identifier.uri | http://hdl.handle.net/10203/42294 | - |
dc.description | 학위논문(석사) - 한국과학기술원 : 응용수학과, 1987.2, [ [ii], 16, [2] p. ; ] | - |
dc.description.abstract | We extend convergence theorems of discrete parameter operator-valued martingale to those of operatorvalued martingale indexed by directed set. We prove that: (1) $L^1$-bounded weak operator-valued martingale indexed by directed set converges in probability to a weak random operator. If it is uniformly integrable on a dense subset of a Hilbert space, then it is closable and converges in $L^1$ mean; (2) If a strong operator-valued martingale indexd by directed set is $L^1$ bounded and its inverse image of a compact positive symmetric operator is bounded in probability, then it converges in probability to a strong random operator. Furthermore, if it is $L^2$-bounded, then it converges to a strong random operator in $L^2$ mean; (3) An operator-valued martingale indexed by directed set which is uniformly integrable and satisfies additional condition converges in probability to a bounded random operator. | eng |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.title | Convergence theorems of operator-valued martingale indexed by directed set | - |
dc.title.alternative | 유향집합을 첨자로 가지는 연산자 치마아팅게일의 수렴성에 관한 연구 | - |
dc.type | Thesis(Master) | - |
dc.identifier.CNRN | 65547/325007 | - |
dc.description.department | 한국과학기술원 : 응용수학과, | - |
dc.identifier.uid | 000851129 | - |
dc.contributor.localauthor | Choi, Bong-Dae | - |
dc.contributor.localauthor | 최봉대 | - |
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