THE SEMIGROUP GOVERNING THE GENERALIZED COX-INGERSOLL-ROSS EQUATION

被引：0
|
作者：
Goldstein, Gisele Ruiz [1 ]
Goldstein, Jerome A. [1 ]
Mininni, Rosa Maria [2 ]
Romanelli, Silvia [2 ]
机构：
[1] Univ Memphis, Dept Math Sci, Memphis, TN 38152 USA
[2] Univ Bari Aldo Moro, Dept Math, Via E Orabona 4, I-70125 Bari, Italy
来源：
ADVANCES IN DIFFERENTIAL EQUATIONS | 2016年 / 21卷 / 3-4期
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D O I：
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中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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, infinity]. 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.
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页码：235 / 264
页数：30
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