6533b7dbfe1ef96bd1270a7c
RESEARCH PRODUCT
From Feynman–Kac formulae to numerical stochastic homogenization in electrical impedance tomography
Petteri PiiroinenMartin Simonsubject
65C05Statistics and Probability65N21stochastic homogenizationquantitative convergence result01 natural sciencesHomogenization (chemistry)78M40general reflecting diffusion process010104 statistics & probabilitysymbols.namesakeFeynman–Kac formula60J4535Q60Applied mathematicsFeynman diagramBoundary value problemSkorohod decomposition0101 mathematicsElectrical impedance tomographyBrownian motionMathematicsrandom conductivity field65N75010102 general mathematicsFeynman–Kac formulaLipschitz continuityBounded functionstochastic forward problemsymbols60J55Statistics Probability and Uncertainty60H30electrical impedance tomographydescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-10-01 | The Annals of Applied Probability |