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Teoriya Veroyatnostei i ee Primeneniya, 1976, Volume 21, Issue 3, Pages 613–620
(Mi tvp3405)
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This article is cited in 5 scientific papers (total in 5 papers)
Short Communications
A representation of some martingales
L. I. Gal'čuk Moscow
Abstract:
Let $X_t=(X_t^1,\dots,X_t^n)$, $0\le t\le 1$, be a continuous square integrable martingale for which the processes $\langle X^i,X^j\rangle_t$, $i,j=1,\dots,n$, are deterministic, and let $(Y_t,\mathscr F_t^X)$ be a square integrable martingale where $\mathscr F_t^X=\sigma\{X_s,s\le t\}$.
In the paper, the representation $\displaystyle Y_t=Y_0+\int_0^t\sum_{i=1}^nf_{s-}^i\,dX_s^i$ is proved where $f_s^i$ are previsible processes with $\displaystyle\mathbf M\int_0^{\infty}\sum_{i,j=1}^nf_s^if_s^jd\langle X^i,X^j\rangle_s<\infty.$
Received: 25.09.1975
Citation:
L. I. Gal'čuk, “A representation of some martingales”, Teor. Veroyatnost. i Primenen., 21:3 (1976), 613–620; Theory Probab. Appl., 21:3 (1977), 599–605
Linking options:
https://www.mathnet.ru/eng/tvp3405 https://www.mathnet.ru/eng/tvp/v21/i3/p613
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Abstract page: | 170 | Full-text PDF : | 122 | First page: | 1 |
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