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Enlightened by the theory of Watanabe [Watanabe S (1987) Analysis of Wiener functionals (Malliavin calculus) and its applications to heat kernels. Ann. Probab. 15:1–39] for analyzing generalized rando...
Enlightened by the theory of Watanabe [Watanabe S (1987) Analysis of Wiener functionals (Malliavin calculus) and its applications to heat kernels. Ann. Probab. 15:1–39] for analyzing generalized rando...
We examine different ways of numerically computing the distribution function of conditional expectations where the conditioning element takes values in a finite or countably infinite outcome space. Bo...
We discuss some properties of conditional expectation operators, and use these facts to prove an interesting counterexample regarding sufficient statistics. In particular, we show that there exists su...
Linear conditional expectations and quadratic conditional variances determine a class of stochastic processes with independent increments. Characterizations of the Wiener, Poisson, gamma, negative ...
Let X and Y be R-valued random variables on a nonatomic probability space (8, 5, P). We give conditions under which Y can be approximated by a conditional expectation of X. In particular, we prove ...
In this work, we present results of Almost Sure Convergence and in Quadratic Mean of the gradient stochastic process for the sequential estimation of a conditional expectation. This work is motived b...

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