AN EVALUATION FORMULA FOR A GENERALIZED CONDITIONAL EXPECTATION WITH TRANSLATION THEOREMS OVER PATHS

IF 0.7 4区 数学 Q2 MATHEMATICS
D. Cho
{"title":"AN EVALUATION FORMULA FOR A GENERALIZED CONDITIONAL EXPECTATION WITH TRANSLATION THEOREMS OVER PATHS","authors":"D. Cho","doi":"10.4134/JKMS.J190133","DOIUrl":null,"url":null,"abstract":". Let C [0 ,T ] denote an analogue of Wiener space, the space of real-valued continuous functions on the interval [0 ,T ]. For a partition 0 = t 0 < t 1 < ··· < t n < t n +1 = T of [0 ,T ], define X n : C [0 ,T ] → R n +1 by X n ( x ) = ( x ( t 0 ) ,x ( t 1 ) ,...,x ( t n )). In this paper we derive a simple evaluation formula for Radon-Nikodym derivatives similar to the conditional expectations of functions on C [0 ,T ] with the conditioning function X n which has a drift and does not contain the present position of paths. As applications of the formula with X n , we evaluate the Radon-Nikodym derivatives of the functions (cid:82) T 0 [ x ( t )] m dλ ( t )( m ∈ N ) and [ (cid:82) T 0 x ( t ) dλ ( t )] 2 on C [0 ,T ], where λ is a complex-valued Borel measure on [0 ,T ]. Finally we derive two translation theorems for the Radon-Nikodym derivatives of the functions on C [0 ,T ].","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"45 1","pages":"451-470"},"PeriodicalIF":0.7000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Korean Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4134/JKMS.J190133","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 3

Abstract

. Let C [0 ,T ] denote an analogue of Wiener space, the space of real-valued continuous functions on the interval [0 ,T ]. For a partition 0 = t 0 < t 1 < ··· < t n < t n +1 = T of [0 ,T ], define X n : C [0 ,T ] → R n +1 by X n ( x ) = ( x ( t 0 ) ,x ( t 1 ) ,...,x ( t n )). In this paper we derive a simple evaluation formula for Radon-Nikodym derivatives similar to the conditional expectations of functions on C [0 ,T ] with the conditioning function X n which has a drift and does not contain the present position of paths. As applications of the formula with X n , we evaluate the Radon-Nikodym derivatives of the functions (cid:82) T 0 [ x ( t )] m dλ ( t )( m ∈ N ) and [ (cid:82) T 0 x ( t ) dλ ( t )] 2 on C [0 ,T ], where λ is a complex-valued Borel measure on [0 ,T ]. Finally we derive two translation theorems for the Radon-Nikodym derivatives of the functions on C [0 ,T ].
具有路径平移定理的广义条件期望的求值公式
。设C [0,T]表示区间[0,T]上的实值连续函数空间的一个类似的Wiener空间。对于划分0 = t 0 < t 1 <···< t n < t n +1 = t ([0, t]),定义X n: C [0, t]→R n +1 × X n (X) = (X (t 0), X (t 1),…(x (t n))本文导出了一个简单的Radon-Nikodym导数的计算公式,类似于C [0,T]上函数的条件期望,条件函数X n具有漂移且不包含路径的当前位置。作为带X n的公式的应用,我们计算了函数(cid:82) t0 [X (T)] m dλ (T)(m∈n)和[(cid:82) t0 X (T) dλ (T)] 2在C [0,T]上的Radon-Nikodym导数,其中λ是[0,T]上的复值Borel测度。最后导出了C [0,T]上函数的Radon-Nikodym导数的两个平移定理。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
CiteScore
1.20
自引率
16.70%
发文量
0
审稿时长
6-12 weeks
期刊介绍: This journal endeavors to publish significant research of broad interests in pure and applied mathematics. One volume is published each year, and each volume consists of six issues (January, March, May, July, September, November).
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信