We construct an estimator based on “signature matching” for differential equations driven by rough paths and we prove its consistency and asymptotic normality. Note that the the Moment Matching estimator is a special case of this estimator.

Model reduction by moment-matching relies upon the availability of so-called moment . If system is nonlinear, computation moments depends on an underlying specific invariance equation, which can be difficult or impossible to solve. This article presents four technical contributions related theo...

Linear goal programming can be used as a complementary technique when local moment matching method up to the second moment gives some negative mass. This could happen when manipulating a discrete or mixed type severity distribution. In that case we can avoid a simple retreat to the first moment and look for an arithmetic distribution with equal mean and the second moment closest to that of the ...

In this paper, we calculate a low order model of linear system large dimension, that matches set high moments the transfer function and achieves pole-zero placement constraints. The satisfying all constraints simultaneously is selected from family parametrized reduced models. parameters are computed solving an explicit algebraic system. Furthermore, construct Loewner matrices given data imposed...