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...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2018-01-01
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| Series: | Mathematical Problems in Engineering |
| Online Access: | http://dx.doi.org/10.1155/2018/9687039 |
| Summary: | 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. |
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| ISSN: | 1024-123X 1563-5147 |