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Motivated by improving mortality tables from human demography databases, weinvestigate statistical inference of a stochastic age-evolving density of apopulation alimented by time inhomogeneous mortality and fertility. Asymptoticsare taken as the size of the population grows within a limited time horizon:the observation gets closer to the solution of the Von Foerster Mc Kendrickequation, and the difficulty lies in controlling simultaneously the stochasticapproximation to the limiting PDE in a suitable sense together with anappropriate parametrisation of the anisotropic solution. In this setting, weprove new concentration inequalities that enable us to implement theGoldenshluger-Lepski algorithm and derive oracle inequalities. We obtainminimax optimality and adaptation over a wide range of anisotropic H\"oldersmoothness classes.

Nonparametric adaptive inference of birth and death models in a large population limit