Applying the self-interacting process approach to high-dimensional MV-SDEs may pose several limitations and challenges. One significant challenge is the computational complexity associated with simulating and analyzing high-dimensional systems. As the dimensionality of the problem increases, the number of particles or interactions in the self-interacting process grows exponentially, leading to a substantial increase in computational cost. This can make it challenging to obtain accurate and efficient approximations of the invariant measure for high-dimensional MV-SDEs. Additionally, the curse of dimensionality may impact the convergence rates of the numerical methods, requiring sophisticated techniques to mitigate these effects. Furthermore, the interpretation and visualization of results in high-dimensional spaces can be challenging, making it harder to gain insights from the approximation methods in practice.