Abstract We establish general “collapse to the mean” principles that provide conditions under which a law-invariant functional reduces an expectation. In convex setting, we retrieve and sharpen known results from literature. However, our also apply beyond setting. illustrate this by providing complete account of for quasiconvex functionals. special cases consistent risk measures Choquet integra...

We consider the efficient quantization of a class of non bandlimited signals, namely the class of discrete time signals that can be recovered from their decimated version. By definition, these signals are cwersampled and it is reasonable to expect that we can reap the same benefits of well known efficient A/D conversion techniques. Indeed, by using appropriate multirate reconstruction schemes, ...

This paper develops an approach to the transient analysis of adaptive filters with data normalization. Among other results, the derivation characterizes the transient behavior of such filters in terms of a linear time-invariant state-space model. The stability of the model then translates into the mean-square stability of the adaptive filters. Likewise, the steady-state operation of the model p...

In this paper, we study asymptotic stability properties of risk-sensitive filters with respect to their initial conditions. In particular, we consider a linear time-invariant systems with initial conditions that are not necessarily Gaussian. We show that in the case of Gaussian initial conditions, the optimal risksensitive filter asymptotically converges to any suboptimal filter initialized wit...

Lars Lindbom, Mikael Sternad and Anders Ahlén Signals and Systems, Uppsala University, PO Box 528, SE-75120, Uppsala, Sweden. [email protected], ms,aa @signal.uu.se Abstract: Adaptation laws with constant gains, that adjust parameters of linear regression models, are investigated. The class of algorithms includes LMS as its simplest member. Closed-form expressions for the tracking MSE...

Approximations of slightly nonlinear systems with linear time-invariant (LTI) models are often used in applications. Here, LTI models that are optimal approximations in the mean-square error sense are studied. It is shown that these models can be very sensitive to small nonlinearities. Furthermore, the significance of the distribution of the input process is discussed. From the examples studied...

In this paper, we study asymptotic stability properties of risk-sensitive lters with respect to their initial conditions. In particular, we consider a linear time-invariant systems with initial conditions that are not necessarily Gaussian. We show that in the case of Gaussian initial conditions, the optimal risk-sensitive lter asymptotically converges to any suboptimal lter initialized with an ...

The least-mean-squares (LMS) algorithm is analysed as a feedback control system. It is shown that despite the fact that LMS is a time-variant system that in fact it behaves much as a linear time-invariant (LTI) closed-loop control system. Therefore, it is possible to treat the LMS algorithm as a control system in the classical sense and define properties such as bandwidth to determine how fast ...