New statistical methods for stochastic processes

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The modeling with stochastic processes has rich applications in physics, biology and finance. The calibration of such stochastic process models based on the available data is essential in order to make the theoretical models accessible for the practitioners. At the same time statistics for stochastic processes poses interesting and challenging mathematical problems. The aim of this research fellowship is to connect modern fields in mathematical statistics and probability theory to obtain new estimation methods and results for diffusions, stochastic partial differential equations and Lévy processes. More specifically, we want to construct adaptive confidence bands for nonparametric volatility estimation in diffusion models and make use of the gained insights to analyze estimators for stochastic partial differential equations. In parallel we want to extend concepts of the statistical learning theory for inference on stochastic processes.