November 8, 2025

Conditional McKean-Vlasov Differential Equations with Common Poissonian Noise: Propagation of Chaos

Key Points

Weak convergence is demonstrated as population size approaches infinity, validating chaos propagation.
Key evidence emphasizes the significance of weak convergence for understanding system behaviors in large populations.
Analysis of McKean-Vlasov differential equations with common Poissonian noise was performed through mathematical formulation.
This study highlights implications for modeling large populations in stochastic systems with collective effects.

Abstract

A model for the evolution of a large population interacting system is considered in which a marked Poisson processes influences their evolution, together with a Brownian motion. Mean field McKean-Vlasov limits of such system are formulated studying first both systems individually. Letting the population size growing to infinite, the weak convergence of the solutions of such systems is proved; in other words, propagation of chaos of such systems is obtained.

Conditional McKean-Vlasov Differential Equations with Common Poissonian Noise: Propagation of Chaos

Key Points

Abstract

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