耦合变分不等式组的概率表示与逼近
Probabilistic Representation and Approximation for Coupled Systems of Variational Inequalities
摘要：
我们的研究致力于变分不等式的耦合系统解的概率表示和数值逼近。解的每个分量的动力学由不同的线性抛物算子驱动，并且在解的所有分量中具有非线性依赖性。这种动态与全局结构约束的解决方案，包括最佳切换问题的实际例子之间的所有组件。本文将这类变分不等式的耦合系统的唯一黏性解解释为最近在[6]中引入的带跳的一维约束倒向随机微分方程的解。在[3]的精神，这种新的表示允许引入一个自然的完全概率的数值方案，这些系统的分辨率。
英文摘要：
Our study is dedicated to the probabilistic representation and numerical approximation of solutions to coupled systems of variational inequalities. The dynamics of each component of the solution is driven by a different linear parabolic operator and suffers a non-linear dependence in all the components of the solution. This dynamics is combined with a global structural constraint between all the components of the solution including the practical example of optimal switching problems. In this paper, we interpret the unique viscosity solution to this type of coupled systems of variational inequalities as the solution to one-dimensional constrained BSDEs with jumps introduced recently in [6]. In the spirit of [3], this new representation allows for the introduction of a natural entirely probabilistic numerical scheme for the resolution of these systems.
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