Publikationsdatum:
2012-10-18
Beschreibung:
In a previous work by the first author with J. Turi [Appl. Math. Optim. 58(1) (2008), 1–27], a stochastic variational inequality has been introduced to model an elasto-plastic oscillator with noise. A major advantage of the stochastic variational inequality is to overcome the need to describe the trajectory by phases (elastic or plastic). This is useful, since the sequence of phases cannot be characterized easily. In particular, when a change of regime occurs, there are numerous small elastic phases which may appear as an artefact of the Wiener process. However, it remains important to have informations on both the elastic and plastic phases. In order to reconcile these contradictory issues, we introduce an approximation of stochastic variational inequalities by imposing artificial small jumps between phases allowing a clear separation of the elastic and plastic regimes. In this work, we prove that the approximate solution converges on any finite time interval, when the size of jumps tends to 0. Content Type Journal Article Pages 171-187 DOI 10.3233/ASY-2012-1109 Authors Alain Bensoussan, International Center for Decision and Risk Analysis, School of Management, University of Texas at Dallas, Richardson, TX, USA Héctor Jasso-Fuentes, Departamento de Matemáticas, Cinvestav-IPN, México, D.F. México. E-mail: hjasso@math.cinvestav.mx Stéphane Menozzi, Université Denis Diderot-Paris 7, Paris, France. E-mail: menozzi@math.univ-paris-diderot.fr Laurent Mertz, Department of Statistics, The Chinese University of Hong Kong, Hong Kong. E-mail: mertz@sta.cuhk.edu.hk Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 80 Journal Issue Volume 80, Number 1-2 / 2012
Print ISSN:
0921-7134
Digitale ISSN:
1875-8576
Thema:
Mathematik
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