Strong convergence of tamed theta scheme for superlinearly growing McKean-Vlasov NSDDEs driven by fractional Brownian motions

TL;DR

This paper investigates the existence, uniqueness, and numerical approximation of superlinearly growing McKean-Vlasov NSDDEs driven by fractional Brownian motion, establishing convergence rates for the proposed scheme.

Contribution

It introduces a tamed theta Euler-Maruyama scheme for these complex equations and proves its convergence rate, advancing numerical methods for fractional stochastic delay equations.

Findings

Existence and uniqueness of solutions via Picard iteration.

Development of a tamed theta Euler-Maruyama scheme.

Proven convergence rate of the numerical scheme.

Abstract

In this article, we study the McKean-Vlasov neutral stochastic differential delay equations driven by fractional Brownian motion with super-linearly growing coefficients, where the Hurst exponent $H\in(1/2,1)$. The existence and uniqueness of the exact solution were shown by the Picard iteration. Besides, we propose a tamed theta Euler-Maruyama scheme for this equation, analyzed the moment boundness and propagation of chaos etc. Moreover, the convergence rate of the numerical scheme is established.