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

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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

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

Dates
First available in Project Euclid: 18 February 2016

Permanent link to this document
https://projecteuclid.org/euclid.ade/1455805258

Mathematical Reviews number (MathSciNet)
MR3461294

Zentralblatt MATH identifier
1341.47051

Subjects
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

Citation

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. https://projecteuclid.org/euclid.ade/1455805258.


Export citation