Approximations of Path-distribution Dependent Stochastic Differential Equations Driven by α-stable Noise

In this work, we show an approximation issue on a class of path-distribution dependent stochastic differential equations driven by α-stable noise, where the drift is singular. The key findings are as follows: (i) we show the regularity of the associated Kolmogorov equation and a deterministic inequality about the jump-diffusion coefficients; (ii) via Zvonkin’s transformation, we show the propagation of chaos and convergence rate of the truncated Euler-Maruyama scheme associated with the interacting particle systems. In contrast to the existing literature, the novelty of this work lies in dealing with path singularity for path-distribution dependent stochastic differential equations with multiplicative noise and selecting the appropriate numerical approximation for the segment process.