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STOCHASTIC HEAT EQUATION ON ALGEBRA OF GENERALIZED FUNCTIONS

Department of Mathematics, Higher School of Sciences and Technologies of Hammam-Sousse, Sousse University, Sousse, Tunisia

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HABIB OUERDIANE

Department of Mathematics, Faculty of Sciences of Tunis, University of Tunis El-Manar, 1060 Tunis, Tunisia

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, and

HAFEDH RGUIGUI

Department of Mathematics, Faculty of Sciences of Tunis, University of Tunis El-Manar, 1060 Tunis, Tunisia

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https://doi.org/10.1142/S0219025712500269Cited by:13 (Source: Crossref)

Abstract

The main objective of this paper is to investigate an extension of the "Volterra-Gross" Laplacian on nuclear algebra of generalized functions. In so doing, without using the renormalization procedure, this extension provides a continuous nuclear realization of the square white noise Lie algebra obtained by Accardi–Franz–Skeide in Ref. 2. An extended-Gross diffusion process driven by a class of Itô stochastic equations is studied, and solution of the related Poisson equations is derived in terms of a suitable λ-potential.

Keywords:

AMSC: 60H40, 46F25

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