Abstract

In this talk we focus on results regarding inverse problems described by nonlinear operator equations both in a deterministic and statistical framework. The last developments in the methodology are reviewed and similarities and di erences related to the nature of the setting are emphasized. Furthermore, a convergence analysis leading to order optimal rates in the deterministic case and order-optimal rates up to a log-factor in the stochastic case for the Lepskii choice of the regularization parameter for a range of smoothness classes and with a milder smallness assumptions is presented. These assumptions are shown to be satisfied by a Volterra-Hammerstein non-linear integral equation that has several applications as population growth model in the population dynamics.

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