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March/April 2016 The semigroup governing the generalized Cox-Ingersoll-Ross equation
Gisele Ruiz Goldstein, Jerome A. Goldstein, Rosa Maria Mininni, Silvia Romanelli
Adv. Differential Equations 21(3/4): 235-264 (March/April 2016).

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.

Citation

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Gisele Ruiz Goldstein. Jerome A. Goldstein. Rosa Maria Mininni. Silvia Romanelli. "The semigroup governing the generalized Cox-Ingersoll-Ross equation." Adv. Differential Equations 21 (3/4) 235 - 264, March/April 2016.

Information

Published: March/April 2016
First available in Project Euclid: 18 February 2016

zbMATH: 1341.47051
MathSciNet: MR3461294

Subjects:
Primary: 35C15 , 35K15 , 47D06 , 91B25

Rights: Copyright © 2016 Khayyam Publishing, Inc.

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Vol.21 • No. 3/4 • March/April 2016
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