On the Rate of Convergence of Weak Euler Approximation for Nondegenerate It\^{o} Diffusion and Jump Processes

The paper studies the rate of convergence of the weak Euler approximation for It^{o} diffusion and jump processes with H"{o}lder-continuous generators. It covers a number of stochastic processes including the nondegenerate diffusion processes and a class of stochastic differential equations driven by stable processes. To estimate the rate of convergence, the existence of a unique solution to the corresponding backward Kolmogorov equation in H"{o}lder space is first proved. It then shows that the Euler scheme yields positive weak order of convergence.