Approximation of finite-dimensional distributions for integrals driven by α-stable Lévy motion

We present a method of numerical approximation for stochastic integrals involving α-stable Lévy motion as an integrator. Constructions of approximate sums are based on the Poissonian series representation of such random measures. The main result gives an estimate of the rate of convergence of finite-dimensional distributions of finite sums approximating such stochastic integrals. Stochastic integrals driven by such measures are of interest in constructions of models for various problems arising in science and engineering, often providing a better description of real life phenomena than their Gaussian counterparts.