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A noise of new type and its generalized functionals

Takeyuki Hida (2011)

Banach Center Publications

The purpose of this paper is to introduce a new noise denoted by P'(u). It has the space parameter u, being compared with the usual noise depending on the time t. We first explain why such a noise arises naturally. Then, we come to the analysis of functionals of this new noise. We shall emphasize the significance of generalized functionals of P'(u), in particular, linear and quadratic.

Central extensions and stochastic processes associated with the Lie algebra of the renormalized higher powers of white noise

Luigi Accardi, Andreas Boukas (2010)

Banach Center Publications

In the first part of the paper we discuss possible definitions of Fock representation of the *-Lie algebra of the Renormalized Higher Powers of White Noise (RHPWN). We propose one definition that avoids the no-go theorems and we show that the vacuum distribution of the analogue of the field operator for the n-th renormalized power of WN defines a continuous binomial process. In the second part of the paper we present without proof our recent results on the central extensions of RHPWN, its subalgebras...

Derivative of the Donsker delta functionals

Herry Pribawanto Suryawan (2019)

Mathematica Bohemica

We prove that derivatives of any finite order of Donsker's delta functionals are well-defined elements in the space of Hida distributions. We also show the convergence to the derivative of Donsker's delta functionals of two different approximations. Finally, we present an existence result of finite product and infinite series of the derivative of the Donsker delta functionals.

Detección de M señales gaussianas utilizando el desarrollo modificado de un proceso estocástico.

Jesús Navarro Moreno, Juan Carlos Ruiz Molina (2001)


Utilizando el desarrollo modificado de un proceso estocástico se propone una nueva metodología, alternativa a la basada en el desarrollo de Karhunen-Loeve, para el problema de detección de M señales Gaussianas en ruido Gaussiano blanco. Las soluciones proporcionadas no presentan el problema del cálculo de los autovalores y autofunciones asociados a la función de covarianza involucrada y son fácilmente implementables desde el punto de vista práctico.

Existence and controllability of fractional-order impulsive stochastic system with infinite delay

Toufik Guendouzi (2013)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

This paper is concerned with the existence and approximate controllability for impulsive fractional-order stochastic infinite delay integro-differential equations in Hilbert space. By using Krasnoselskii's fixed point theorem with stochastic analysis theory, we derive a new set of sufficient conditions for the approximate controllability of impulsive fractional stochastic system under the assumption that the corresponding linear system is approximately controllable. Finally, an example is provided...

Infinite dimensional Gegenbauer functionals

Abdessatar Barhoumi, Habib Ouerdiane, Anis Riahi (2007)

Banach Center Publications

he paper is devoted to investigation of Gegenbauer white noise functionals. A particular attention is paid to the construction of the infinite dimensional Gegenbauer white noise measure β , via the Bochner-Minlos theorem, on a suitable nuclear triple. Then we give the chaos decomposition of the L²-space with respect to the measure β by using the so-called β-type Wick product.

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