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Analyticity of the Cox–Ingersoll–Ross semigroup

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Abstract

We study the analyticity of the Cox–Ingersoll–Ross semigroup generated by

$$\begin{aligned} A_r u=\nu ^2 xu''+\gamma u'+\beta x u'-rx u, \end{aligned}$$

in spaces of continuous functions on \([0,+\infty )\) and we provide the full description of the domain of the generator.

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References

  1. Angenent, S.: Local existence and regularity for a class of degenerate parabolic equations. Math. Ann. 280, 465–482 (1988)

    Article  MathSciNet  Google Scholar 

  2. Bátkai, A., Fijavž, M.K., Rhandi, A.: Positive Operator Semigroups. Birkhäuser/Springer, Cham (2017)

    Book  Google Scholar 

  3. Campiti, M., Metafune, G.: Ventcel’s boundary conditions and analytic semigroups. Arch. Math. 70, 377–390 (1998)

    Article  MathSciNet  Google Scholar 

  4. Cox, J.C., Ingersoll, J.E., Ross, S.A.: A theory of the term structure of interest rates. Econometrica 53, 385–407 (1985)

    Article  MathSciNet  Google Scholar 

  5. Engel, K.-J., Nagel, R.: One-Parameter Semigroups for Linear Evolution Equations. Springer, Berlin (2000)

    MATH  Google Scholar 

  6. Feller, W.: The parabolic differential equations and the associated semigroups of transformations. Ann. Math. (2) 55, 468–519 (1952)

    Article  MathSciNet  Google Scholar 

  7. Fornaro, S., Manco, V.: On the domain of some ordinary differential operators in spaces of continuous functions. Arch. Math. 82, 335–343 (2004)

    Article  MathSciNet  Google Scholar 

  8. Goldstein, G.Ruiz, Goldstein, J.A., Mininni, R.M., Romanelli, S.: The semigroup governing the generalized Cox–Ingersoll–Ross equation. Adv. Differ. Equ. 21(3–4), 235–264 (2016)

    MathSciNet  MATH  Google Scholar 

  9. Goldstein, G.R., Goldstein, J.A., Mininni, R.M., Romanelli, S.: A generalized Cox-Ingersoll-Ross equation with growing initial conditions. DCDS-S (2019). https://doi.org/10.3934/dcdss.2020085

    Article  MATH  Google Scholar 

  10. Metafune, G.: Analiticity for some degenerate one-dimensional evolution equations. Studia Math. 127(3), 251–276 (1998)

    Article  MathSciNet  Google Scholar 

  11. Metafune, G., Priola, E.: Some classes of non-analytic Markov semigroups. J. Math. Anal. Appl. 294, 596–613 (2004)

    Article  MathSciNet  Google Scholar 

  12. Metafune, G., Prüss, J., Rhandi, A., Schnaubelt, R.: \(L^p\)-regularity for elliptic operators with unbounded coefficients. Adv. Differ. Equ. 10, 1131–1164 (2005)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Matematica “Felice Casorati”, Università degli Studi di Pavia, 27100, Pavia, Italy

    S. Fornaro

  2. Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Università del Salento, C.P.193, 73100, Lecce, Italy

    G. Metafune

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  1. S. Fornaro
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  2. G. Metafune
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Correspondence to G. Metafune.

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Fornaro, S., Metafune, G. Analyticity of the Cox–Ingersoll–Ross semigroup. Positivity 24, 915–931 (2020). https://doi.org/10.1007/s11117-019-00716-x

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  • DOI: https://doi.org/10.1007/s11117-019-00716-x

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