臺灣博碩士論文加值系統

布朗泛函以布朗運動隨機積分來表示是可被稱之為克拉克公式。在本論文中，我們致力於廣義白噪音泛函之克拉克公式表示。以廣義觀點來說，在區間I，如果存在一個核KF使得 F = E[F] + ∫I KF (t)dB(t), 等式經由S-轉換後等式兩邊相等，如此一來，一個廣義白噪音泛函就可用克拉克表示式來表述。在本文末節，我們給予一些例子來說明廣義白噪音泛函之克拉克表示式。

The representation of functionals of Brownian motion in terms of stochastic integral with respect to Brownian motion is known as Clark formula. In this paper, we are devoted to the derivation of Clark formula for a given generalized white noise functional. A generalized white noise functional F is said to have a Clark representation in the generalized sense on an interval I if there exist a kernel KF such that
F = E[F] + ∫I KF(t) dB(t), where the equality holds in the the generalized sense or, equivalently, the equality holds under the S-transform. Examples of Clark representation of generalized white noise functional are given in this paper.

中文摘要 ii
英文摘要 iii
1 Introduction 1
2 Test and generalized white noise functionals 2
3 The Clark formula for white noise functionals 4
4 Example 7
References 17

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