On the Integral Solutions of the Pdes Related to Some Urn Models

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Project title

Code/計畫編號

NSC97-2119-M019-001

Translated Name/計畫中文名

與Urn模型有關的方程的積分型式解的研究

Project Coordinator/計畫主持人

Hua-Huai Chern

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Computer Science and Engineering

Website

https://www.grb.gov.tw/search/planDetail?id=1657263

Year

2008

Start date/計畫起

01-08-2008

Expected Completion/計畫迄

31-07-2009

Bugetid/研究經費

239千元

ResearchField/研究領域

數學
資訊科學--軟體

此次計畫的內容是延續過去的研究計畫裡，在對透過Urn models 所描繪的應用問題的分析中，幾個尚未釐清與完成分析求解的核心問題的持續研究。這類未能完全解決的問題，主要是跟是否滿足在罈模型描繪上的平衡條件及消減條件有關的。有別於主要的機率分析論述，透過微分方程式進行刻畫的論述，在許多的類型上已經獲致相當深入的刻畫成果亦成為解決與Urn models 有關問題上一種非常有效的論述。為了能達成對尚未解決的類型問題提出可能的有效分析，筆者沿用近來採用的求解論述─對刻畫方程求取積分型式解的作法─企圖對此類問題進行更完整的刻畫與研究；此外，當能順利地求得出對應的積分型式解後，如何發展出有效的直接求算上或是替代的漸近上的求算，因而讓極限法則的推論能更透明容易些，亦是採行這套論述時必須探究的問題。最後，在考慮多色球模型時所衍生的多維度上的問題，除了在少數問題上，因為其問題本身所具有的特殊性，而得以完成分析，是以在這方面的研究工作及成果仍有待持續關注與努力探究中"In this project, we aim to take further investigation on those unsolved or partially resolvable problems characterized via urn models. Such problems appear when the urn models are constrained to the so-called imbalanced and diminishing conditions. Supplementary to the preferential approach, the probabilistic approach, the current developing approach by means of ODEs or PDES shows its power and efficiency in doing analysis on certain types of urn models. For the sake of proposing a more complete, effective and deeper characterization on such class of problems, we utilize the newly-adopted method—finding the solution in integral form—to carry out the investigations. Moreover, as the proper solution in integral form is thus and so obtained, how to go along for the effectively direct or indirectly asymptotical computations on such solution so as to extract the limit laws as easier and transparent as possible is an important issue, too. Last but not the least, when the multi-colored urn models are considered, only few problems, those are quite peculiar intrinsically, are thoroughly solvable, there are still a lot of problems deserved to be studied."

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On the Integral Solutions of the Pdes Related to Some Urn Models

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