Convergence of Probability Densities using Approximate Models for Forward and Inverse Problems in Uncertainty Quantification: Extensions to L^p

2020/01/13 by Butler, Troy, Wildey, Tim, Zhang, Wenjuan
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2001.04369

Abstract

A previous study analyzed the convergence of probability densities for forward and inverse problems when a sequence of approximate maps between model inputs and outputs converges in L^∞. This work generalizes the analysis to cases where the approximate maps converge in L^p for any 1≤ p < ∞. Specifically, under the assumption that the approximate maps converge in L^p, the convergence of probability density functions solving either forward or inverse problems is proven in L^q where the value of 1≤ q

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