Multidimensional Stable Driven McKean-Vlasov SDEs with Distributional Interaction Kernel: Critical Thresholds and Related Models

TL;DR

This paper investigates the well-posedness of multidimensional stable-driven McKean-Vlasov SDEs with distributional interaction kernels, emphasizing the role of initial condition smoothness and identifying critical thresholds relevant to physical and biological models.

Contribution

It advances the understanding of well-posedness for these SDEs by analyzing the impact of Besov smoothness and establishing critical thresholds for stability in models with stable noise.

Findings

Identified critical thresholds for stability based on initial condition smoothness.

Extended the approach to address models in physics and biology with stable noise.

Provided density estimates influenced by Besov regularity.

Abstract

In this work we continue to investigate well-posedness for stable driven McKean-Vlasov SDEs with distributional interaction kernel following the approach introduced in [8]. We specifically focus on the impact of the Besov smoothness of the initial condition and quantify how it affects the corresponding density estimates for the SDE. In particular, we manage to attain some critical thresholds allowing to revisit/address in a stable noise setting some concrete physical and biological models.