ERRATUM: White-Noise Representations in Stochastic Realization Theory

Sparse Representations and Realization Theory

We present some results obtained recently in signal processing in the so-called “sparse representations” domain and indicate how they can be applied to a very specific and limited problem in realization theory. This is mainly to bring these type of results to the knowledge of this community. Other applications in order estimation for instance are potentially feasible. The basic problem is the f...

Toward a Theory of Nonlinear Stochastic Realization

Stochastic algorithms for discontinuous multiplicative white noise.

Stochastic differential equations with multiplicative noise need a mathematical prescription due to different interpretations of the stochastic integral. This fact implies specific algorithms to perform numerical integrations or simulations of the stochastic trajectories. Moreover, if the multiplicative noise function is not continuous then the standard algorithms cannot be used. We present an ...

Stochastic heat equation with white-noise drift

White Noise Theory and Its Applications

White noise does not mean unwanted sounds, but it is useful for science as well as for daily life through the mathematical theory that we shall explain in this note. The white noise theory is an analysis of functions of continuously many variables and is naturally developing into the modern theory of stochastic analysis. It applies to things of all sizes; quantum dynamics, statistical mechanics...