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

Daniel Hernández-Hernández; Joshué Helí Ricalde-Guerrero

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arXiv · 2308.11564

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

Daniel Hernández-Hernández·Joshué Helí Ricalde-Guerrero

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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.

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Daniel Hernández-Hernández, Joshué Helí Ricalde-Guerrero. 2023-08-22. Conditional McKean-Vlasov Differential Equations with Common Poissonian Noise: Propagation of Chaos. https://arxiv.org/abs/2308.11564

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