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DFG Forschergruppe 1735 - TP5:
"Identifiability and structural inference for high-dimensional diffusion matrices"

DFG Forschergruppe 1735: "Structural Inference in Statistics: Adaption and Efficiency
Teilprojekt 5: "Identifiability and structural inference for high-dimensional diffusion matrices"

Zeitraum: 2012 - 2015, Projektleiterin: Frau Prof. Dr. Angelika Rohde

The proposed research project treats statistical inference for sparse high-dimensional diffusion matrices. Sparsity constraints induce a considerable complexity reduction which renders the statistical procedures meaningful even if the dimension of the diffusion is large compared to the time interval of observations. Diffusion models are employed more and more often in applications like biology, finance or physics and the problem of estimating the diffusion matrix is at the same time an important issue for applications and a challenge for the mathematical analysis due to new observation structures and dependencies. Although there exists an appreciable amount of results on statistical analysis on scalar diffusions, the statistical literature on multi-dimensional or even high-dimensional diffusion processes is very limited. One key issue will therefore also be questions of identifiability and model reduction, e.g. allowing for higher-dimensional driving Brownian motions when this allows for a very sparse diffusion matrix representation. Throughout, we shall assume that the structural constraints are satisfied over time while the actual values may change smoothly in time. This results in a challenging simultaneous adaptation problem. Our focus is then on the estimation of entries and functionals of the diffusion matrix. Our analysis will allow more fundamental insight even for more classical i.i.d. situations.