Integral representation theorem for classical Wiener space について

Words near each other

Dictionary Lists

mini英和辞書

翻訳と辞書　辞書検索 [ 開発暫定版 ]

スポンサードリンク

Integral representation theorem for classical Wiener space ：ウィキペディア英語版

Integral representation theorem for classical Wiener space
In mathematics, the integral representation theorem for classical Wiener space is a result in the fields of measure theory and stochastic analysis. Essentially, it shows how to decompose a function on classical Wiener space into the sum of its expected value and an Itō integral.
==Statement of the theorem==

Let

); \mathbb)

(or simply

C_

for short) be classical Wiener space with classical Wiener measure

\gamma

. If

F \in L^ (C_; \mathbb)

, then there exists a unique Itō integrable process

) \times C_ \to \mathbb

(i.e. in

L^ (B)

, where

B

is canonical Brownian motion) such that
:

F(\sigma) = \int_ \gamma (p) + \int_^ \alpha^ (\sigma)_ \, \mathrm \sigma_

for

\gamma

-almost all

\sigma \in C_

.
In the above,
*

\int_ \gamma (p) = \mathbb ()

is the expected value of

F

; and
* the integral

\int_^ \cdots\, \mathrm \sigma_

is an Itō integral.
The proof of the integral representation theorem requires the Clark-Ocone theorem from the Malliavin calculus.

抄文引用元・出典: フリー百科事典『ウィキペディア（Wikipedia）』
■ウィキペディアで「Integral representation theorem for classical Wiener space」の詳細全文を読む

スポンサードリンク

翻訳と辞書 : 翻訳のためのインターネットリソース