On some errors related to the graduation of measuring instruments
Probability
2007-05-23 v2
Abstract
The error on a real quantity Y due to the graduation of the measuring instrument may be represented, when the graduation is regular and fines down, by a Dirichlet form on R whose square field operator do not depend on the probability law of Y as soon as this law possesses a continuous density. This feature is related to the "arbitrary functions principle" (Poincar\'{e}, Hopf). We give extensions of this property to multivariate case and infinite dimensional case for approximations of the Brownian motion. We use a Girsanov theorem for Dirichlet forms which has its own interest. Connections are given with discretization of stochastic differential equations.
Cite
@article{arxiv.math/0610355,
title = {On some errors related to the graduation of measuring instruments},
author = {Nicolas Bouleau},
journal= {arXiv preprint arXiv:math/0610355},
year = {2007}
}
Comments
23p