The semigroup governing the generalized cox-ingersoll-ross equation
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,∞]. 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.
Advances in Differential Equations
Goldstein, G., Goldstein, J., Mininni, R., & Romanelli, S. (2016). The semigroup governing the generalized cox-ingersoll-ross equation. Advances in Differential Equations, 21 (3-4), 235-264. Retrieved from https://digitalcommons.memphis.edu/facpubs/5948