Minimal asymptotic errors for L_2-global approximation of SDEs with additive Poisson noise

We study minimal asymptotic errors for strong global approximation of stochastic differential equations driven by the homogeneous Poisson process N with unknown intensity $\lambda$> 0. We consider two cases of sampling of N: equidistant and nonequidistant. In both cases, we show that the minimal error tends to zero like $C n^{−1/2}$, where C is the average in time of the jump coefficient and n is the number of evaluations of N. However, the asymptotic constant C when the equidistant sampling is used can be considerably larger than the asymptotic constant in the nonuniform sampling case. We also provide a construction of methods that asymptotically achieve the established minimal errors.