On estimation of random variables via the martingale convergence theorem
Conditional expectation and the martingale convergence theorem are frequently used in attempts to estimate a random variable as a function of other random variables. Examples are exhibited which illustrate difficulties arising from a careless approach to these techniques. Real- valued random variables, including a Gaussian random variable, are constructed such that the martingale convergence theorem, or any scheme based on conditional expectation, can fail to be of any value whatsoever in estimating them.
scientific article; zbMATH DE number 4054786