STOCHASTIC HEAT EQUATION ON ALGEBRA OF GENERALIZED FUNCTIONS-Reference-Cited by-同舟云学术

STOCHASTIC HEAT EQUATION ON ALGEBRA OF GENERALIZED FUNCTIONS

Published:2012-12 Issue:04 Volume:15 Page:1250026
ISSN:0219-0257
Container-title:Infinite Dimensional Analysis, Quantum Probability and Related Topics
language:en
Short-container-title:Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

Author:

BARHOUMI ABDESSATAR¹,OUERDIANE HABIB²,RGUIGUI HAFEDH²

Affiliation:

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

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

Abstract

The main objective of this paper is to investigate an extension [Formula: see text] 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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Mathematical Physics,Statistics and Probability,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219025712500269

Reference37 articles.

1. A QUANTUM APPROACH TO LAPLACE OPERATORS

2. EXOTIC LAPLACIANS AND ASSOCIATED STOCHASTIC PROCESSES

3. L. Accardi and O. G. Smolyanov, Mathematical Approach to Fluctuations II (World Scientific, Singapore, 1995) pp. 31–47.

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