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.