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In a paper, I find the expression "Let $$\{X(Y_k) | Y_k\}_{k=0,1, \cdots}$$ be mutually independent"

Q: What does this notation mean? Does somebody know it? Is it some kind of conditional independence? How do I have to define it well?

For every $d \in R^n$, $X(d): \Omega \to R$ is a random variable, $Y_k: \Omega \to R^n$.

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    what is $X$ there? is it a measurable function?2011-08-17
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    @Gortaur $X$ and $Y_k$ are random variables ($X$ stands for the measurement noise of a physical system with parameters $Y_k$)2011-08-17
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    What is then $X(Y)$? The co-domain of $Y$ is not a subset of the domain of $X$.2011-08-17
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    I can also post the link to the paper as well, I mean equation (2.4) on page 1162 in http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=47894892011-08-17
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    Hmmm... *Available to subscribers and IEEE members.*2011-08-17
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    The paper: http://www.jhuapl.edu/spsa/PDF-SPSA/Spall_A_Stochastic_Approximation.PDF // My guess: this means that the random variables X(y) are independent for different values of y, where each X(y) is the random variable T defined by T(omega)=X(y)(omega) for every omega in Omega.2011-08-17
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    @Didier Thanks for finding the better source for the paper :) You write only $y$, but you would still consider $\hat{\theta}_k$ in the paper to be a random variable? (after all after the initialization for $k=0$ in the definition of the subsequent $\hat{\theta}_k$ random variables turn up) [No confusion - The $\hat{\theta}_k$ in the paper plays the role of $Y_k$ here]2011-08-17

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