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

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Functional Analysis and Evolution Equations

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(ℝd), we prove the generation results in L p(ℝd) for p ∈ [1,+∞]. These results have several consequences in connection with the financial applications [3, 11].

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Author information

Authors and Affiliations

  1. Dipartimento di Sistemi ed Istituzioni per l’Economia, P.zza del Santuario 19, I-67040, Roio Poggio (AQ), Italy

    Massimiliano Giuli

  2. Dipartimento di Scienze Economiche e Aziendali, Viale Pola 12, I-00198, Roma, Italy

    Fausto Gozzi

  3. Dipartimento di Studi Economico-Finanziari e Metodi Quantitativi, Via Columbia 2, I-00133, Roma, Italy

    Roberto Monte

  4. Dipartimento di Matematica Ulisse Dini, Viale Morgagni 67A, I-50134, Firenze, Italy

    Vincenzo Vespri

Authors
  1. Massimiliano Giuli
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  2. Fausto Gozzi
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  3. Roberto Monte
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  4. Vincenzo Vespri
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Editor information

Editors and Affiliations

  1. Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057, Zürich, Switzerland

    Herbert Amann

  2. Abteilung Angewandte Analysis, Universität Ulm, 89069, Ulm, Germany

    Wolfgang Arendt

  3. Fachbereich Mathematik, Technische Universität Darmstadt, Schloßgartenstr. 7, 64289, Darmstadt, Germany

    Matthias Hieber

  4. Department of Mathematics, Louisiana State University, Baton Rouge, LA, 70803, USA

    Frank M. Neubrander

  5. Université de Valenciennes et du Hainaut Cambrésis, Le Mont Houy, 59313, Valenciennes Cedex 9, France

    Serge Nicaise

  6. Laboratoire de Mathématiques Pures et Appliquées — LMPA “Joseph Liouville”, Université du Littoral-Côte d’Opale, 50, rue F. Buisson, 62228, Calais Cedex, France

    Joachim von Below

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© 2007 Birkhäuser Verlag Basel/Switzerland

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Giuli, M., Gozzi, F., Monte, R., Vespri, V. (2007). Generation of Analytic Semigroups and Domain Characterization for Degenerate Elliptic Operators with Unbounded Coefficients Arising in Financial Mathematics. Part II. In: Amann, H., Arendt, W., Hieber, M., Neubrander, F.M., Nicaise, S., von Below, J. (eds) Functional Analysis and Evolution Equations. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7794-6_21

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