The main goal of this paper is to investigate the multi-parameter stability result for a stochastic fractional differential variational inequality with Lévy jump (SFDVI with Lévy jump) under some mild conditions. We verify that Mosco convergence of the perturbed set implies point convergence of the projection onto the Hilbert space consisting of special stochastic processes whose range is the perturbed set. Moreover, by using the projection method and some inequality techniques, we establish a strong convergence result for the solution of SFDVI with Lévy jump when the mappings and constraint set are both perturbed. Finally, we apply the stability results to the spatial price equilibrium problem and the multi-agent optimization problem in stochastic environments.

中文翻译：

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Lévy jump 的随机分数阶微分变分不等式的稳定性


本文的主要目标是研究在一些温和条件下具有 Lévy 跳跃的随机分数阶微分变分不等式（SFDVI 与 Lévy 跳跃）的多参数稳定性结果。我们验证了扰动集的 Mosco 收敛意味着投影到希尔伯特空间上的点收敛，该空间由特殊的随机过程组成，其范围是扰动集。此外，通过使用投影方法和一些不等式技术，当映射和约束集都受到扰动时，我们为 SFDVI 与 Lévy jump 的解建立了一个强收敛结果。最后，我们将稳定性结果应用于随机环境中的空间价格均衡问题和多智能体优化问题。