  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.

Functional Analysis;Probability