# A simple approach to proving the existence, uniqueness, and strong and weak convergence rates for a broad class of McKean-Vlasov equations

@article{HajiAli2021ASA, title={A simple approach to proving the existence, uniqueness, and strong and weak convergence rates for a broad class of McKean-Vlasov equations}, author={Abdul-Lateef Haji-Ali and Hrakon Hoel and Ra{\'u}l Tempone}, journal={ArXiv}, year={2021}, volume={abs/2101.00886} }

By employing a system of interacting stochastic particles as an approximation of the McKean–Vlasov equation and utilizing classical stochastic analysis tools, namely Itô’s formula and Kolmogorov–Chentsov continuity theorem, we prove the existence and uniqueness of strong solutions for a broad class of McKean–Vlasov equations. Considering an increasing number of particles in the approximating stochastic particle system, we also prove the L strong convergence rate and derive the weak convergence…

## 3 Citations

### Single Level Importance Sampling for McKean-Vlasov Stochastic Differential Equations

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This paper investigates Monte Carlo methods to estimate probabilities of rare events associated with solutions to the d -dimensional McKean-Vlasov stochastic diﬀerential equation. The equation is…

### Double Loop Monte Carlo Estimator with Importance Sampling for McKean-Vlasov Stochastic Differential Equation

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This paper investigates Monte Carlo methods to estimate probabilities of rare events associated with solutions to the d -dimensional McKean-Vlasov stochastic diﬀerential equation. The equation is…

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This work combines multilevel Monte Carlo methods with importance sampling (IS) to estimate rare event quantities that can be expressed as the expectation of a Lipschitz observable of the solution to…

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