Optimal Rate of Convergence for Vector-valued Wiener-Itô Integral
Huiping Chen · Latin American Journal of Probability and Mathematical Statistics · 2024
We investigate the optimal rate of convergence in the multidimensional normal approximation of vector-valued Wiener-Itô integrals whose components all belong to a fixed Wiener chaos with coinciding orders.By combining Malliavin calculus, Stein's method for normal approximation and the method of cumulants, we obtain the optimal rate of convergence with respect to a suitable smooth distance.As applications, we derive the optimal rates of convergence for complex Wiener-Itô integrals, vector-valued Wiener-Itô integrals with kernels of step functions and vector-valued Toeplitz quadratic functionals.