Positive Harris recurrence and exponential ergodicity of the basic affine jump-diffusion. Issue 1 (2nd January 2016)

• Record Type: Journal Article
• Authors: Jin, Peng; Rüdiger, Barbara; Trabelsi, Chiraz
• Is Part Of: Stochastic analysis and applications. Volume 34:Issue 1(2016)
• Page Start: 75
• Page End: 95
• Publication Date: 2016-01-02
• Subjects: Affine process -- basic affine jump-diffusion -- exponential ergodicity -- Harris recurrence -- stochastic differential equation; Primary 60H10 -- Secondary 60J60; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2015.1105752
• Languages: English
• ISSNs: 0736-2994

Abstract

Abstract: In this article, we find the transition densities of the basic affine jump-diffusion (BAJD), which has been introduced by Duffie and Gârleanu as an extension of the CIR model with jumps. We prove the positive Harris recurrence and exponential ergodicity of the BAJD. Furthermore, we prove that the unique invariant probability measure π of the BAJD is absolutely continuous with respect to the Lebesgue measure and we also derive a closed-form formula for the density function of π.