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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/54033


    Title: 隨機函數及其應用之研究
    Other Titles: A Study of the Random Functional and Its Applications
    Authors: 姜志銘
    Contributors: 政治大學應用數學系
    行政院國家科學委員會
    Keywords: 貝氏無母數;Ferguson-Dirichlet過程;隨機動差;c-特徵函數
    Date: 2006
    Issue Date: 2012-10-24 16:13:30 (UTC+8)
    Abstract: Ferguson-Dirichlet過程已廣泛地應用於許多領域，特別是在貝氏無母數問題方面，目前已慢慢變成熱門的研究主題。本研究中，我們將使用-特徵函數(Jiang, 1988)之反演公式(Jiang and Kuo, 2005, 2006)來研究Ferguson-Dirichlet過程的隨機函數。同時，我們將進一步研究對應於某些重要的Ferguson-Dirichlet過程的新的隨機動差。 c Jiang, Dickey, and Kuo (2004)將單維度的-特徵函數擴展到多維度的-特徵函數，然而這個多維度-特徵函數的反演公式仍為未知，我們將先研究這個反演公式，接下來再研究Ferguson-Dirichlet過程下的多維度隨機函數。我們也將特別研究當Ferguson-Dirichlet過程在球表面或橢圓體表面上的隨機函數。這會是Jiang, Dickey, and Kuo (2004)結果的一個重要延伸。 ccc Ferguson-Dirichlet過程應用的模擬與數值計算是相當重要的課題。我們將研究簡易的計算方式以使Ferguson-Dirichlet過程的應用更加有效率。
    Jiang, Dickey, and Kuo (2004) give the multivariate c-characteristic function and show that it has properties similar to those of the multivariate Fourier transformation. This new transformation can be useful when a distribution is difficult to deal with using Fourier transformation or traditional characteristic function. In this paper, we first give the multivariate c-characteristic function of the random functional of a Ferguson-Dirichlet process on the unit ball. We then find out its probability density function using properties of the multivariate c-characteristic function. This new result in three-dimension would generalize the two-dimensional result given by Jiang (1991).
    Relation: 基礎研究
    學術補助
    研究期間:9508~ 9607
    研究經費:714仟元
    Data Type: report
    Appears in Collections:[Department of Mathematical Sciences] NSC Projects

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