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

2023/02/20 by P. -E. Chaudru de Raynal, de Raynal, P. -E Chaudru, Jean-François Jabir +3
Economics, Econometrics and Finance · Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2302.09900

openalex publication_date 2023/02/20 · openalex created_date 2023/02/22 · openalex updated_date 2026/08/01

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.

Citations

• Symmetric Stable Laws and Stable-Like Jump-Diffusions
• Heat kernel of supercritical SDEs with unbounded drifts
• Well-posedness of stochastic heat equation with distributional drift and skew stochastic heat equation
• Second order fractional mean-field SDEs with singular kernels and measure initial data

Related

• Multidimensional Stable driven McKean-Vlasov SDEs with distributional interaction kernel -- a regularization by noise perspective
• On well-posedness of stable-driven McKean-Vlasov stochastic differential equations with Besov interaction kernel of non-positive regularity
• Well-Posedness for McKean-Vlasov SDEs with Distribution Dependent Stable Noises
• Well-Posedness for McKean-Vlasov SDEs Driven by Multiplicative Stable Noises
• Strong and weak well-posedness of McKean-Vlasov SDEs driven by α-stable processes under unified condition