A Distributional Identity for the Bivariate Brownian Bridge: A Nontensor Gaussian Field

A Distributional Identity for the Bivariate Brownian Bridge: A Nontensor Gaussian Field

The bivariate Brownian bridge, a nontensor Gaussian Field, is defined by B(t1,t2)=W(t1,t2)W(1,1)=0=W(t1,t2)-t1t2W(1,1), where t1,t2∈I=[0,1] and W(t1,t2) is a Brownian sheet. We obtain a distributional identity, a consequence of the Karhunen-Loève expansion for the bivariate Brownian bridge by Fredho...

Full description

Bibliographic Details
Main Author: Xiaohui Ai
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2018/9687039
id doaj-88072f9e78dc49a5a5db4b79f632550c
record_format Article
spelling doaj-88072f9e78dc49a5a5db4b79f632550c2020-11-24T22:26:44ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472018-01-01201810.1155/2018/96870399687039A Distributional Identity for the Bivariate Brownian Bridge: A Nontensor Gaussian FieldXiaohui Ai0Mathematics School, Jilin University, Changchun 130012, ChinaThe bivariate Brownian bridge, a nontensor Gaussian Field, is defined by B(t1,t2)=W(t1,t2)W(1,1)=0=W(t1,t2)-t1t2W(1,1), where t1,t2∈I=[0,1] and W(t1,t2) is a Brownian sheet. We obtain a distributional identity, a consequence of the Karhunen-Loève expansion for the bivariate Brownian bridge by Fredholm integral equation and Laplace transform approach.http://dx.doi.org/10.1155/2018/9687039
collection DOAJ
language English
format Article
sources DOAJ
author Xiaohui Ai
spellingShingle Xiaohui Ai
A Distributional Identity for the Bivariate Brownian Bridge: A Nontensor Gaussian Field
Mathematical Problems in Engineering
author_facet Xiaohui Ai
author_sort Xiaohui Ai
title A Distributional Identity for the Bivariate Brownian Bridge: A Nontensor Gaussian Field
title_short A Distributional Identity for the Bivariate Brownian Bridge: A Nontensor Gaussian Field
title_full A Distributional Identity for the Bivariate Brownian Bridge: A Nontensor Gaussian Field
title_fullStr A Distributional Identity for the Bivariate Brownian Bridge: A Nontensor Gaussian Field
title_full_unstemmed A Distributional Identity for the Bivariate Brownian Bridge: A Nontensor Gaussian Field
title_sort distributional identity for the bivariate brownian bridge: a nontensor gaussian field
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2018-01-01
description The bivariate Brownian bridge, a nontensor Gaussian Field, is defined by B(t1,t2)=W(t1,t2)W(1,1)=0=W(t1,t2)-t1t2W(1,1), where t1,t2∈I=[0,1] and W(t1,t2) is a Brownian sheet. We obtain a distributional identity, a consequence of the Karhunen-Loève expansion for the bivariate Brownian bridge by Fredholm integral equation and Laplace transform approach.
url http://dx.doi.org/10.1155/2018/9687039
work_keys_str_mv AT xiaohuiai adistributionalidentityforthebivariatebrownianbridgeanontensorgaussianfield
AT xiaohuiai distributionalidentityforthebivariatebrownianbridgeanontensorgaussianfield
_version_ 1725751897929809920

Similar Items