A note on local asymptotic behaviour for Brownian motion in Banach spaces
In this paper we obtain an integral characterization of a two-sided upper function for Brownian motion in a real separable Banach space. This characterization generalizes that of Jain and Taylor [2] where B=ℝn. The integral test obtained involves the index of a mean zero Gaussian measure on the Bana...
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| Format: | Article |
| Language: | English |
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Wiley
1979-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171279000491 |
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| _version_ | 1832547500050874368 |
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| author | Mou-Hsiung Chang |
| author_facet | Mou-Hsiung Chang |
| author_sort | Mou-Hsiung Chang |
| collection | DOAJ |
| description | In this paper we obtain an integral characterization of a two-sided upper function for Brownian motion in a real separable Banach space. This characterization generalizes that of Jain and Taylor [2] where B=ℝn. The integral test obtained involves the index of a mean zero Gaussian measure on the Banach space, which is due to Kuelbs [3]. The special case that when B is itself a real separable Hilbert space is also illustrated. |
| format | Article |
| id | doaj-art-44a2ef9437444afa8cb20c245256f836 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1979-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-44a2ef9437444afa8cb20c245256f8362025-02-03T06:44:36ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251979-01-012466967610.1155/S0161171279000491A note on local asymptotic behaviour for Brownian motion in Banach spacesMou-Hsiung Chang0Department of Mathematics, The University of Alabama in Huntsville, Huntsville 35807, Alabama, USAIn this paper we obtain an integral characterization of a two-sided upper function for Brownian motion in a real separable Banach space. This characterization generalizes that of Jain and Taylor [2] where B=ℝn. The integral test obtained involves the index of a mean zero Gaussian measure on the Banach space, which is due to Kuelbs [3]. The special case that when B is itself a real separable Hilbert space is also illustrated.http://dx.doi.org/10.1155/S0161171279000491Gaussian measures on B-spaceabstract Wiener spacescovariace operatorsBrownian motion in B-spaceupper and lower functionsintegral test. |
| spellingShingle | Mou-Hsiung Chang A note on local asymptotic behaviour for Brownian motion in Banach spaces International Journal of Mathematics and Mathematical Sciences Gaussian measures on B-space abstract Wiener spaces covariace operators Brownian motion in B-space upper and lower functions integral test. |
| title | A note on local asymptotic behaviour for Brownian motion in Banach spaces |
| title_full | A note on local asymptotic behaviour for Brownian motion in Banach spaces |
| title_fullStr | A note on local asymptotic behaviour for Brownian motion in Banach spaces |
| title_full_unstemmed | A note on local asymptotic behaviour for Brownian motion in Banach spaces |
| title_short | A note on local asymptotic behaviour for Brownian motion in Banach spaces |
| title_sort | note on local asymptotic behaviour for brownian motion in banach spaces |
| topic | Gaussian measures on B-space abstract Wiener spaces covariace operators Brownian motion in B-space upper and lower functions integral test. |
| url | http://dx.doi.org/10.1155/S0161171279000491 |
| work_keys_str_mv | AT mouhsiungchang anoteonlocalasymptoticbehaviourforbrownianmotioninbanachspaces AT mouhsiungchang noteonlocalasymptoticbehaviourforbrownianmotioninbanachspaces |