發(fā)布時(shí)間：2018-02-26 02:23

  本文關(guān)鍵詞： 復(fù)可分希爾伯特空間 復(fù)Isonormal高斯過程 復(fù)Hermite多項(xiàng)式 復(fù)Malliavin導(dǎo)算子 光滑隨機(jī)變量 Wiener-It?chaos分解 廣義萊布尼茨法則　出處：《湖南科技大學(xué)》2016年碩士論文　論文類型：學(xué)位論文

【摘要】：以實(shí)可分的希爾伯特空間存在實(shí)Isonormal高斯過程為基礎(chǔ),在復(fù)可分的希爾伯特空間上建立了一個(gè)復(fù)Isonormal高斯過程。再從此復(fù)Isonormal高斯過程出發(fā),運(yùn)用復(fù)Hermite多項(xiàng)式定義了關(guān)于復(fù)Isonormal高斯過程的Wiener-It?chaos,并且通過復(fù)Hermite多項(xiàng)式正交性的性質(zhì),給出了平方可積空間的Wiener-It?chaos分解。接著在復(fù)Isonormal高斯過程上建立了光滑的隨機(jī)變量函數(shù)類,進(jìn)而在光滑的隨機(jī)變量函數(shù)類中研究定義復(fù)Malliavin導(dǎo)算子。本論文的核心就是要說明復(fù)Malliavin導(dǎo)算子在光滑的隨機(jī)變量函數(shù)類中是可閉化的。為此,先證明了實(shí)Isonormal高斯過程Malliavin導(dǎo)算子的可閉性,在這個(gè)研究過程中,發(fā)現(xiàn)并得到了Malliavin導(dǎo)算子的廣義萊布尼茨法則,以及通過以Hermite多項(xiàng)式作為工具,得到散度算子的表示定理以及分部積分公式。作為一個(gè)應(yīng)用,通過類比的方法,證明了復(fù)Isonormal高斯過程Malliavin導(dǎo)算子的可閉性。
[Abstract]:Based on the existence of real Isonormal Gao Si process in real separable Hilbert space, a complex Isonormal Gao Si process is established on the complex separable Hilbert space. The complex Hermite polynomials are used to define the Wiener-ITT process of the complex Isonormal Gao Si process. By using the property of orthogonality of complex Hermite polynomials, this paper gives the space of square integrable space Wiener-It? Chaos decomposition. Then in the complex Isonormal Gao Si process, the smooth class of random variable functions is established. The core of this paper is to show that the complex Malliavin derivative operator is closed in the class of smooth random variable functions. This paper first proves the closeness of the Malliavin derivative operator of real Isonormal Gao Si process. In this study, the generalized Leibniz rule of Malliavin derivative operator is found and obtained, and the Hermite polynomial is used as a tool. The representation theorem and integral formula of divergence operator are obtained. As an application, the closeness of Malliavin derivative operator of complex Isonormal Gao Si process is proved by analogy.
【學(xué)位授予單位】：湖南科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：O177

【參考文獻(xiàn)】

相關(guān)碩士學(xué)位論文 前1條

1 季媛媛;復(fù)Malliavin算子及其應(yīng)用[D];湖南科技大學(xué);2015年

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本文編號：1536147