模拟具有消失跳跃的弹塑性问题的随机变分不等式的渐近分析
Asymptotic Analysis of Stochastic Variational Inequalities Modeling an Elasto-Plastic Problem with Vanishing Jumps
AI总结：
本文通过引入人工小跳跃近似随机变分不等式，证明当跳跃尺寸趋于零时近似解在任意有限时间区间上收敛，从而调和了弹塑性振荡器模型中相位难以描述与需要相位信息之间的矛盾。
摘要：
在第一作者与J. Turi之前的工作（AMO, 08）中，引入了一个随机变分不等式来模拟带噪声的弹塑性振荡器。随机变分不等式的一个主要优点是克服了通过相位（弹性或塑性）描述轨迹的需要。这很有用，因为相位的序列不易刻画。特别是，存在许多小的弹性相位，它们可能作为维纳过程的伪影出现。然而，获取这些相位的信息仍然很重要。为了调和这些矛盾的问题，我们通过引入相位之间的人工小跳跃来近似随机变分不等式，从而允许相位的清晰分离。在这项工作中，我们证明了当跳跃尺寸趋于0时，近似解在任何有限时间区间上收敛。
英文摘要：
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.
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