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 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 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)