Generation of Analytic Semigroups and Domain Characterization for Degenerate Elliptic Operators with Unbounded Coefficients Arising in Financial Mathematics. Part II
Massimiliano Giuli, Fausto Gozzi, Roberto Monte, Vincenzo Vesprı · Birkhäuser Basel eBooks · 2007
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 finance. The generation property is proved by assuming some compensation conditions among the coefficients and applying a suitable modification 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 ∈ [1,+∞]. These results have several consequences in connection with the financial applications [3, 11].