## Advances in Differential Equations

### The semigroup governing the generalized Cox-Ingersoll-Ross equation

#### 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

#### 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