Convergence of the Random Batch Method for Interacting Particle Systems Driven by Fractional Brownian Motion

In this paper, the random batch method for solving interacting particle systems driven by fractional Brownian motion with Hurst parameter $H ∈ (0,1)$ is introduced. The random batch method is an efficient technique that significantly reduces the computational cost of simulating interacting particle systems. A detailed error analysis of the method is conducted, accompanied by rigorous derivations of upper bounds for these errors. Numerical experiments are performed to verify the theoretical results, demonstrating the effectiveness and efficiency of the proposed method.