Chow Y.S., Teicher H., Probability Theory: Independence, Interchangeability and Martingales, 2nd ed., Springer-Verlag, 1988. Home/Search Document Not in Database Summary Related Articles Check |
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The Almost Equivalence of Pairwise and Mutual Independence and the.. - Sun (1998) (Correct)
....f t are almost surely independent in n tuple, i.e. f t 1 ; f t 2 ; f t n are mutually independent for L# n almost all t 1 ; t 2 ; t n 2T n . The idea of exchangeability has a wide range of applications in both pure and applied probability (see, for example, A] Bi] [CT] and Pairwise and mutual independence 431 [K] which is commonly studied in the sequential setting. A sequence C of random variables is said to be exchangeable if for any n 1, the joint distribution of any n random variables from C depends only on n but not on the particular choice and ....
....by f # . Moreover, for L# almost all t 2 T , the distribution of f t is simply the distribution induced by f viewed as a random variable on the Loeb product space. The notion of exchangeability has already been linked to conditional independence through the classical de Finetti theorem (see [CT], p. 222, and [K] The nal result of this section relates exchangeability to unconditional independence. It shows that the two notions are in fact dual to each other in the sense that almost exchangeability of the random variables in a hypernite process is equivalent to almost independence of the ....
Chow, Y.H. and H. Teicher, H. Probability Theory: independence, interchangeability and martingales, Springer-Verlag, New York, 1978.
The Role of Completeness in Convergence of - Evolutionary Algorithms Eugene (Correct)
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Chow Y.S., Teicher H., Probability Theory: Independence, Interchangeability and Martingales, 2nd ed., Springer-Verlag, 1988.
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