| A REMARK ON A BMO MARTINGALE |
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| 作者姓名： | 向开南 |
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| 作者单位： | Institute of Applied Mathematics，Academia Sinica，Beijing 100080，China; Department of probability and statistics，Peking University，Beijing 100871，China |
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| 基金项目： | Research supported in part by CNSF, Tianyuan foundation,，the Mathematical Center of Ministry of Education |
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| 摘 要： | Let M = (Mt,Ft) be a uniformly integrable continuous martingale with MO = 0. For1 5 p < cot we setIIMllBMO. = '3p IIEIMoo ~ MTIplFT]]'/Pll.,where the supremum is taken over all stopping times T.Set BMO. = {M: IIMllBMO. < co}. It is well known that BMO. = BMO, (VI S p 5 q).F'urthermore, all 11.llBMO. norms are equivalent andIIi ~~if;llMllBMO. = SUP T P(T < co)i'where the supremum is taken over all stopping times T satisfying P(T < co) > 0. In the laterwe shall simply …
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A REMARK ON A BMO MARTINGALE |
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| XIANG Kainan.A REMARK ON A BMO MARTINGALE[J].Acta Mathematica Scientia,2000,20(4). |
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| Authors: | XIANG Kainan |
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| Abstract: | In this paper, a negative answer to a question raised by Durrett(1984)1] about a BMO martingale is given. |
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| Keywords: | Continuous martingale uniformly integrable BMO martingale |
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