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arXiv · 1502.04353

From Feynman-Kac Formulae to Numerical Stochastic Homogenization in Electrical Impedance Tomography

Petteri Piiroinen·Martin Simon
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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.

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Petteri Piiroinen, Martin Simon. 2015-02-15. From Feynman-Kac Formulae to Numerical Stochastic Homogenization in Electrical Impedance Tomography. https://arxiv.org/abs/1502.04353

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