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International Journal of Analysis
Volume 2016 (2016), Article ID 5963420, 11 pages
http://dx.doi.org/10.1155/2016/5963420
Research Article

Some Nonlinear Stochastic Cauchy Problems with Generalized Stochastic Processes

Equipe Analyse Algébrique Non Linéaire, Université des Antilles, Campus de Schoelcher, BP 7209, 97275 Schoelcher Cedex, Martinique

Received 4 July 2016; Accepted 25 July 2016

Academic Editor: Ying Hu

Copyright © 2016 Victor Dévoué. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study some nonlinear stochastic Cauchy problems in the framework of the -algebras. We adapt the definitions to this framework. By means of suitable regularizations, we define associated generalized problems. We use our previous results about the wave equation in canonical form to obtain generalized solutions. We compare the generalized solutions with the classical ones when they exist.