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In a previous work by the first author with J. Turi (AMO, 08), a stochasticvariational inequality has been introduced to model an elasto-plasticoscillator with noise. A major advantage of the stochastic variationalinequality is to overcome the need to describe the trajectory by phases(elastic or plastic). This is useful, since the sequence of phases cannot becharacterized easily. In particular, there are numerous small elastic phaseswhich may appear as an artefact of the Wiener process. However, it remainsimportant to have informations on these phases. In order to reconcile thesecontradictory issues, we introduce an approximation of stochastic variationalinequalities by imposing artificial small jumps between phases allowing a clearseparation of the phases. In this work, we prove that the approximate solutionconverges on any finite time interval, when the size of jumps tends to 0.

Asymptotic Analysis of Stochastic Variational Inequalities Modeling an Elasto-Plastic Problem with Vanishing Jumps