Please use this identifier to cite or link to this item:
https://ah.lib.nccu.edu.tw/handle/140.119/120128
DC Field | Value | Language |
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dc.contributor | 應數系 | |
dc.creator | 林光賢 | |
dc.creator | Lin, Kuang Hsien | |
dc.creator | 陳天進 | |
dc.creator | Chen, Ten Ging | |
dc.creator | Yang, Ling-Huey | |
dc.date | 1993-03 | |
dc.date.accessioned | 2018-09-25T08:22:01Z | - |
dc.date.available | 2018-09-25T08:22:01Z | - |
dc.date.issued | 2018-09-25T08:22:01Z | - |
dc.identifier.uri | http://nccur.lib.nccu.edu.tw/handle/140.119/120128 | - |
dc.description.abstract | Let $S_n=\\sum^n_{j=1}a_jY_j$, $n\\geq 1$, where $\\{Y_n,\\ n\\geq 1\\}$ is a sequence of i.i.d. random variables with the generalized Petersburg distribution $P\\{Y_1=q^{-k}\\}=pq^{k-1}$, $k\\geq 1$, where $0<p=1-q<1$ and $a_n,\\ n\\geq 1$, are positive constants with $(\\sum^n_{j=1}a_j)/\\max_{1\\leq j\\leq n}a_j\\to\\infty$. The main result asserts that $S_n/M_n\\overset P\\to\\rightarrow 1$, where $$M_n=\\sup\\Big\\{x\\colon\\ \\sum^n_{j=1}a_jEY_1I(a_jY_1\\leq x)\\geq x\\Big\\},\\quad n\\geq 1,$$\n\n thereby generalizing a result of A. Adler and the reviewer [Bull. Inst. Math. Acad. Sinica 17 (1989), no. 3, 211–227; MR1042179] obtained for the particular choice $a_n=n^\\alpha$, $n\\geq 1$, where $\\alpha>-1$. This problem has the following interesting interpretation. Suppose a player wins $a_nY_n$ dollars during the $n$th game in a sequence of generalized Petersburg games. If $M_n=\\sum^n_{j=1}m_j$ represents the accumulated entrance fees for playing the first $n$ games, then $S_n/M_n\\overset P\\to\\rightarrow 1$ is the assertation that $\\{m_n,\\ n\\geq 1\\}$ is a "fair solution in the weak sense to the games``. | en_US |
dc.format.extent | 161 bytes | - |
dc.format.mimetype | text/html | - |
dc.relation | Chinese Journal of Mathematics,21(1),21-31 | |
dc.relation | AMS MathSciNet:MR1209488 | |
dc.title | On the ""fair`` games problem for the weighted generalized Petersburg games | |
dc.type | article | |
item.grantfulltext | restricted | - |
item.fulltext | With Fulltext | - |
item.openairetype | article | - |
item.cerifentitytype | Publications | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
Appears in Collections: | 期刊論文 |
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