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Generation of Analytic Semigroups and Domain Characterization for Degenerate Elliptic Operators with Unbounded Coefficients Arising in Financial Mathematics. Part II

In: Functional Analysis and Evolution Equations

Author

Listed:
  • Massimiliano Giuli

    (Dipartimento di Sistemi ed Istituzioni per l’Economia)

  • Fausto Gozzi

    (Dipartimento di Scienze Economiche e Aziendali)

  • Roberto Monte

    (Dipartimento di Studi Economico-Finanziari e Metodi Quantitativi)

  • Vincenzo Vespri

    (Dipartimento di Matematica Ulisse Dini)

Abstract

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].

Suggested Citation

  • Massimiliano Giuli & Fausto Gozzi & Roberto Monte & Vincenzo Vespri, 2007. "Generation of Analytic Semigroups and Domain Characterization for Degenerate Elliptic Operators with Unbounded Coefficients Arising in Financial Mathematics. Part II," Springer Books, in: Herbert Amann & Wolfgang Arendt & Matthias Hieber & Frank M. Neubrander & Serge Nicaise & Joachim vo (ed.), Functional Analysis and Evolution Equations, pages 315-330, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7643-7794-6_21
    DOI: 10.1007/978-3-7643-7794-6_21
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