| dc.contributor.advisor | 林光賢 | zh_TW |
| dc.contributor.author (Authors) | 楊玲惠 | zh_TW |
| dc.creator (作者) | 楊玲惠 | zh_TW |
| dc.date (日期) | 1990 | en_US |
| dc.date (日期) | 1989 | en_US |
| dc.date.accessioned | 3-May-2016 14:17:35 (UTC+8) | - |
| dc.date.available | 3-May-2016 14:17:35 (UTC+8) | - |
| dc.date.issued (上傳時間) | 3-May-2016 14:17:35 (UTC+8) | - |
| dc.identifier (Other Identifiers) | B2002005452 | en_US |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/90187 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 應用數學系 | zh_TW |
| dc.description.abstract (摘要) | 令Sn=Σj =1najYj ，其{Yn,n≧1}是具有相同分布的獨立隨機變數序列，且{an , n≧1}為正值實數數列。考慮一連串的比賽遊戲，以anYn表示參與者於第n次比賽時，所獲得的”利益”;且假設欲參與第n次比賽遊戲時，須預先支付賭注mn。在本文中，我們證明:若比賽遊戲採用的是”Generalized Petersburg Games”,即p{Y1=q-k}=pqk-1,0<p=1-q<1,k≧1;且若正值實數數列{an,n≧1}滿足 | zh_TW |
| dc.description.abstract (摘要) | Let Sn=?_(j=1)^( n)??a_j Y_j ?, n≧1,where{Yn, n≧1}are i.i.d. r.v.’s and{an,n≧1}are real numbers. Interpreting an Yn as a player’s winnings from the n-th game,a natural question is whether there is an entrance fee mn to the n-th game such that Sn / Mn → 1 in pr. where Mn= ?_(j=1)^( n)?mj.The Purpose of this paper is to study a generalization of the classical Petersburg game for the weighted i..i.d case. That is, for a sequence{ an,n≧1} of real numbers and i.i.d.r.v.’s { Yn, n≧1}with P{ Y1=q-k}=pqk-1, 0<p=1-q<1, k≧1,find conditions on {an,n≧1}which ensure the existence of constants {Mn, n≧1} for which Sn / Mn－1 in pr. obtains. It is shown that when an≧0, An=1,2,3,..... | en_US |
| dc.description.tableofcontents | Ⅰ Introduction ................1-3 Ⅱ Results...............4-15 References...............16-17 | zh_TW |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#B2002005452 | en_US |
| dc.title (題名) | 有關chow-robbins的"公正"遊戲問題之探討 | zh_TW |
| dc.title (題名) | ON THE CHOW-ROBINS "FAIR" GAMES PROBLEM | en_US |
| dc.type (資料類型) | thesis | en_US |
| dc.relation.reference (參考文獻) | [ 1] A. Adler and A. Rosalsky , On the Chow-Robbins " fair “ games problem, Bulletin of the institute of mathematics academia sinica . , 17 (1989) ) 211-227 [ 2 ] Y. S. Chow and H. Robbins, On sums of independent random variables with Infinite moments and “fair “ games) Proc. Nat. Acad. Sci. U.S.A.,47(1961) , 330-.335 . [ 3 ] Y. S. Chow and H. Teicher , Probability Theory : Independence , Interchangeability , Mrartingale , Springer-Verlag, New York, 1988 . [ 4] W. Feller 1 Note on the law of large numbers and “ fair" games, Ann.Math. Statist. , 16 (1945) , 301-304 . [ 5] W. Feller. , A limit theorem for random variables with infinite moments, Amer. J. Math. , 68 (1946) ,257-262 . [ 6] W. Feller. , An Intruductin to Probability Theory and Its Applications, Vol I, 3rded. , John Wiley, New York, 1968 . [ 7 ] W. Feller. , An Intruductin to Probability Theory and Its Applications, Vol II, 2nded. , John Wiley, New York, 1971 . [ 8] B. Jamison, S. Orey and W. Pruitt, Convergence of weighted averages of independent random variables, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete ,14 (1965) , 40--44 . [ 9] R. A. Maller, Relative stability and the strong law of large numbers, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete , 43 (1978) , 141-148 . [10J B. A. Rogozin , Relatively stable Walks , Theor. Probability Appl. , 21(1976) ,375--379 . | zh_TW |
