ASYMPTOTIC ANALYSIS OF STOCHASTIC VARIATIONAL INEQUALITIES MODELING AN ELASTO-PLASTIC PROBLEM WITH VANISHING JUMPS

Alain Bensoussan (1) , Hector Jasso Fuentes (2) , Laurent Mertz (3) , Stephane Menozzi (4)

1 University of Texas at Dallas - Department of Computer Science [Dallas]
2 Departamento de Matemáticas del Cinvestav-IPN
3 LJLL - Laboratoire Jacques-Louis Lions
4 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

In a previous work by the first author with J. Turi (AMO, 08), 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, there are numerous small elastic phases which may appear as an artefact of the Wiener process. However, it remains important to have informations on these 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 phases. In this work, we prove that the approximate solution converges on any finite time interval, when the size of jumps tends to 0.

Mots clés: Stochastic Variational Inequalities; Elasto-Plasticiy; vanishing jumps

Domaines: Analyse numérique [math.NA]; Probabilités [math.PR]

Alain Bensoussan, Hector Jasso Fuentes, Laurent Mertz, Stephane Menozzi. ASYMPTOTIC ANALYSIS OF STOCHASTIC VARIATIONAL INEQUALITIES MODELING AN ELASTO-PLASTIC PROBLEM WITH VANISHING JUMPS. Asymptotic Analysis, 2012, 80 (1-2), pp.171-187. ⟨hal-00653721⟩