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A particle method for McKean-Vlasov equation with common noise
Abstract
The McKean-Vlasov equation with common noise can be discretized in two steps: first in time using the Euler scheme, and then in space through a particle method, leveraging the propagation of chaos property. Under suitable regularity assumptions—Hölder continuity in time and Lipschitz continuity in both the state and measure arguments—convergence rates are established for both the Euler scheme and the particle method. These results extend previous analyses to the setting with common noise. Finally, the effectiveness of the approach can be illustrated through two simulation examples: a modified conditional Ornstein-Uhlenbeck process with common noise and an interbank market model.
