From Feynman-Kac Formulae to Numerical Stochastic Homogenization in Electrical Impedance Tomography
Abstract
In this paper, we use the theory of symmetric Dirichlet forms to derive Feynman-Kac formulae for the forward problem of electrical impedance tomography with possibly anisotropic, merely measurable conductivities corresponding to different electrode models on bounded Lipschitz domains. Subsequently, we employ these Feynman-Kac formulae to rigorously justify stochastic homogenization in the case of a stochastic boundary value problem arising from an inverse anomaly detection problem. Motivated by this theoretical result, we prove an estimate for the speed of convergence of the projected mean-square displacement of the underlying process which may serve as the theoretical foundation for the development of new scalable stochastic numerical homogenization schemes.
Keywords
Cite
@article{arxiv.1502.04353,
title = {From Feynman-Kac Formulae to Numerical Stochastic Homogenization in Electrical Impedance Tomography},
author = {Petteri Piiroinen and Martin Simon},
journal= {arXiv preprint arXiv:1502.04353},
year = {2015}
}