To the parametric identification of Markov diffusions; the use of the maximum quadratic variation functional

Statistics of Markov diffusions is relatively well developed, nowadays. In particular, there exist strong mathematical results allowing parametric identification in the case, where the datum is one continuous sample path of a process to be identified. These results, however, exploit such specific properties of Markov diffusions, like the quadratic variation, or the martingale property. In practical situations, the recorded data are usually discretized. Even if continuous recordings are made, they never have a non-zero quadratic variation. This paper addresses the problems arising in utilization of such data in adjustment of an appropriate Markov-diffusion-type model to the data at hand. Some numerical experiments are reported. In this way the most important problems are exhibited, and some indications are derived concerning the effectiveness of the modelling in dependence on the discretization step.