Advances in Differential Equations

The semigroup governing the generalized Cox-Ingersoll-Ross equation

Gisele Ruiz Goldstein, Jerome A. Goldstein, Rosa Maria Mininni, and Silvia Romanelli

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The semigroup of a generalized initial value problem including, as a particular case, the Cox-Ingersoll-Ross (CIR) equation for the price of a zero-coupon bond, is studied on spaces of continuous functions on $[0,\infty]$. The main result is the first proof of the strong continuity of the CIR semigroup. We also derive a semi-explicit representation of the semigroup and a Feynman-Kac type formula, in a generalized sense, for the unique solution of the CIR initial value problem as a useful tool for understanding additional properties of the solution itself. The Feynman-Kac type formula is the second main result of this paper.

Article information

Adv. Differential Equations, Volume 21, Number 3/4 (2016), 235-264.

First available in Project Euclid: 18 February 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 35K15: Initial value problems for second-order parabolic equations 35C15: Integral representations of solutions 91B25: Asset pricing models


Goldstein, Gisele Ruiz; Goldstein, Jerome A.; Mininni, Rosa Maria; Romanelli, Silvia. The semigroup governing the generalized Cox-Ingersoll-Ross equation. Adv. Differential Equations 21 (2016), no. 3/4, 235--264.

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