Regularity of Solutions of SDEs Driven by Lévy Processes

In this chapter, we consider strong solutions of Itä diffusions driven by Lévy noise and we study their smoothness related to Malliavin differentiability. The next chapter will be devoted to the study of the smoothness of the probability distributions associated to the solutions. This application of the Malliavin calculus gave origin to its introduction [158]. Within the study of Itä diffusions driven by Brownian noise, we can refer to the recent monographies, e.g., [53, 160, 169, 212] and the references there in. As for the study within the Lévy type of noise, we can refer to, e.g., [35, 118, 221] and references therein. In this short chapter, we present only some fundamental results.