Search results for "65N75"

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From Feynman–Kac formulae to numerical stochastic homogenization in electrical impedance tomography

2016

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 de…

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 tomographyThe Annals of Applied Probability
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Exact simulation of first exit times for one-dimensional diffusion processes

2019

International audience; The simulation of exit times for diffusion processes is a challenging task since it concerns many applications in different fields like mathematical finance, neuroscience, reliability horizontal ellipsis The usual procedure is to use discretization schemes which unfortunately introduce some error in the target distribution. Our aim is to present a new algorithm which simulates exactly the exit time for one-dimensional diffusions. This acceptance-rejection algorithm requires to simulate exactly the exit time of the Brownian motion on one side and the Brownian position at a given time, constrained not to have exit before, on the other side. Crucial tools in this study …

Girsanov theoremand phrases: Exit timeDiscretizationsecondary: 65N75Exit time Brownian motion diffusion processes Girsanov’s transformation rejection sampling exact simulation randomized algorithm conditioned Brownian motion.MSC 65C05 65N75 60G40Exit time01 natural sciencesGirsanov’s transformationrandomized algorithm010104 statistics & probabilityrejection samplingGirsanov's transformationexact simulationFOS: MathematicsApplied mathematicsMathematics - Numerical Analysis0101 mathematicsConvergent seriesBrownian motion60G40MathematicsNumerical AnalysisApplied MathematicsMathematical financeRejection samplingProbability (math.PR)diffusion processesNumerical Analysis (math.NA)conditioned Brownian motionRandomized algorithm010101 applied mathematics[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]Computational MathematicsModeling and Simulationconditioned Brownian motion 2010 AMS subject classifications: primary 65C05Brownian motionRandom variableMathematics - ProbabilityAnalysis[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
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