We consider Volterra Gaussian processes on [0, T ], where T > 0 is a fixed time horizon. These are processes of type Xt = R t 0 zX(t, s)dWs, t ∈ [0, T ], where zX is a square-integrable kernel, and W is a standard Brownian motion. An example is fractional Brownian motion. By using classical techniques from operator theory, we derive measure-preserving transformations of X, and their inherently ...

New developments in nonlinear dynamical systems are permitting Volterra and Wiener nonlinear functional series representations to be optimally approximated by artificial neural networks, which are capable of adaptation, learning and evolution by training with or without supervision.The framework based on Generalized Fock Space, enabling these developments is briefly reviewed. In particular, the...

a new ARX-Laguerre representation is recently built to model the dynamics of complex processes [1, 2]. The ARX-Laguerre models have proven their ability to accurately suit the behavior of systems. In this work, the model is exploited to diagnose the system by detecting its defaults. In this paper we build a proportional observer based on the ARX-Laguerre model. Therefore, the designed observer ...

A Laguerre minimal surface is an immersed surface in R being an extremal of the functional ∫ (H/K− 1)dA. In the present paper, we prove that any ruled Laguerre minimal surface distinct from a plane is up to motion a convolution of the helicoid x = y tan z, the cycloid r(t) = (t− sin t, 1−cos t, 0) and the Plücker conoid (ax+ by) = z(x+y) for some a, b ∈ R. To achieve invariance under Laguerre t...

a new approach is introduced to estimate the formal information of neurons. formal information, mainly discusses about the aspects of the response that is related to the stimulus. estimation is based on introducing a mathematical nonlinear model with hammerstein-wiener system estimator. this method of system identification consists of three blocks to completely describe the nonlinearity of inpu...

We consider an ensemble which interpolates the Laguerre orthogonal ensemble and the Laguerre symplectic ensemble. This interpolating ensemble was introduced earlier by the author and Rains in connection with a last passage percolation model with a symmetry condition. In this paper, we obtain a Painelevé V expression for the distribution of the rightmost particle of the interpolating ensemble. S...

A stair Laguerre pseudospectral method is proposed for numerical solutions of differential equations on the half line. Some approximation results are established. A stair Laguerre pseudospcetral scheme is constructed for a model problem. The convergence is proved. The numerical results show that this new method provides much more accurate numerical results than the standard Laguerre spectral me...

Stable and efficient spectral methods using Laguerre functions are proposed and analyzed for model elliptic equations on regular unbounded domains. It is shown that spectral-Galerkin approximations based on Laguerre functions are stable and convergent with spectral accuracy in the usual (not weighted) Sobolev spaces. Efficient, accurate, and well-conditioned algorithms using Laguerre functions ...

reliability wiener number is a modification of the original wiener number in which probabilities are assigned to edges yielding a natural model in which there are some (or all) bonds in the molecule that are not static. various probabilities naturally allow modelling different types of chemical bonds because chemical bonds are of different types and it is well-known that under certain condition...