Stability for a stochastic fractional differential variational inequality with L\'{e}vy jump

TL;DR

This paper studies the stability of solutions to stochastic fractional differential variational inequalities with Lévy jumps, establishing convergence results and applying them to economic and multi-agent optimization problems.

Contribution

It introduces new stability analysis for SFDVI with Lévy jumps, linking set convergence to solution convergence under perturbations.

Findings

Mosco convergence implies point convergence of projections.

Strong convergence of solutions under perturbations.

Applications to spatial price equilibrium and multi-agent optimization.

Abstract

The main goal of this paper is to investigate the multi-parameter stability result for a stochastic fractional differential variational inequality with L\'{e}vy jump (SFDVI with L\'{e}vy 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 L\'{e}vy 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.