Generation of analytic semigroups and domain characterization for degenerate elliptic operators with unbounded coefficients arising in financial mathematics. II

This paper is devoted to study the generation of analytic semigroup for a family of degenerate elliptic operators (with unbounded coefficients) which includes well known operators arising in mathematical nance. The generation property is proved by assuming some compensation conditions among the coecients and applying a suitable modication of the techniques developed in [16]. Using the results proved in [11] concerning the generation in the space L^2(R^d), we prove the generation results in L^p(R^d) for p in [1;+\infty]. These results have several consequences in connection with the nancial applications [3,11].