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We consider interest rate models where the forward rates are allowed to be driven by a multidimensional Wiener process as well as by a marked point process. Assuming a deterministic volatility structure, and using ideas from systems and control theory, we investigate when the input-output map generated by such a model can be realized by a finite dimensional(More)
We present a new parametrization of inner functions based on the Schur algorithm. We make use of state space formulas (in practice we obtain a new parametrization of observable pairs). The main advantage of our parametrization is that for each chart the observability gramian is constant: this leads to a very good behavior in some approximation problems.
We investigate here the interpolation conditions connected to an interpolating function Q obtained as a Linear Fractional Transformation of another function S. In general, the degree of Q is equal to the number of interpolating conditions plus the degree of S. We show that, if the degree of Q is strictly less that this quantity, there is a number of(More)
We consider the symmetric Darlington synthesis of a p × p rational symmetric Schur function S with the constraint that the extension is of size 2p × 2p. Under the assumption that S is strictly contractive in at least one point of the imaginary axis, we determine the minimal McMillan degree of the extension. In particular, we show that it is generically(More)
We consider a new state-space parametrization for linear time series models: data driven coordinates (DDC), which provides an atlas for the manifold of (stable) p × m transfer functions of fixed McMillan degree n. Hence, DDC has similar desirable properties as more traditional overlapping parametrizations and better than classical canonical forms. Moreover,(More)
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