Square variation of Brownian paths in Banach spaces
It is known that if {W(t), 0≤t≤1} is a standard Brownian motion in ℝ then limn→∞∑i=12n|W(i/2n)−W((i−1)/2n)|2=1 almost surely. We generalize this celebrated theorem of Levy to Brownian motion in real separable Banach spaces.
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| Format: | Article |
| Language: | English |
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Wiley
1982-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S016117128200057X |
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| _version_ | 1832567503615688704 |
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| author | Mou-Hsiung Chang |
| author_facet | Mou-Hsiung Chang |
| author_sort | Mou-Hsiung Chang |
| collection | DOAJ |
| description | It is known that if {W(t), 0≤t≤1} is a standard Brownian motion in ℝ then limn→∞∑i=12n|W(i/2n)−W((i−1)/2n)|2=1 almost surely. We generalize this celebrated theorem of Levy to Brownian motion in real separable Banach spaces. |
| format | Article |
| id | doaj-art-336a0f9ae50345dab8ec69751fe64591 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1982-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-336a0f9ae50345dab8ec69751fe645912025-02-03T01:01:16ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251982-01-015360560710.1155/S016117128200057XSquare variation of Brownian paths in Banach spacesMou-Hsiung Chang0Department of Mathematics, University of Alabama in Huntsville, Huntsville 35899, Alabama, USAIt is known that if {W(t), 0≤t≤1} is a standard Brownian motion in ℝ then limn→∞∑i=12n|W(i/2n)−W((i−1)/2n)|2=1 almost surely. We generalize this celebrated theorem of Levy to Brownian motion in real separable Banach spaces.http://dx.doi.org/10.1155/S016117128200057XGaussian measuresabstract Wiener spaceBrownian motion in Banach spacessquare variation of Brownian paths. |
| spellingShingle | Mou-Hsiung Chang Square variation of Brownian paths in Banach spaces International Journal of Mathematics and Mathematical Sciences Gaussian measures abstract Wiener space Brownian motion in Banach spaces square variation of Brownian paths. |
| title | Square variation of Brownian paths in Banach spaces |
| title_full | Square variation of Brownian paths in Banach spaces |
| title_fullStr | Square variation of Brownian paths in Banach spaces |
| title_full_unstemmed | Square variation of Brownian paths in Banach spaces |
| title_short | Square variation of Brownian paths in Banach spaces |
| title_sort | square variation of brownian paths in banach spaces |
| topic | Gaussian measures abstract Wiener space Brownian motion in Banach spaces square variation of Brownian paths. |
| url | http://dx.doi.org/10.1155/S016117128200057X |
| work_keys_str_mv | AT mouhsiungchang squarevariationofbrownianpathsinbanachspaces |