When and how an error yields a Dirichlet form
Abstract
We consider a random variable $Y$ and approximations $Y_n$, defined on the same probability space with values in the same measurable space as $Y$. We are interested in situations where the approximations $Y_n$ allow to define a Dirichlet form in the space $L^2(P_Y)$ where $P_Y$ is the law of $Y$. Our approach consists in studying both biases and variances. The article attempts to propose a general theoretical framework. It is illustrated by several examples.
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