Asymptotic Expansions of Transition Densities for Hybrid Jump-diffusions
- Cite this article as:
- Liu, Y. & Yin, G. Acta Mathematicae Applicatae Sinica, English Series (2004) 20: 1. doi:10.1007/s10255-004-0143-5
A class of hybrid jump diffusions modulated by a Markov chain is considered in this work. The motivation stems from insurance risk models, and emerging applications in production planning and wireless communications. The models are hybrid in that they involve both continuous dynamics and discrete events. Under suitable conditions, asymptotic expansions of the transition densities for the underlying processes are developed. The formal expansions are validated and the error bounds obtained.
KeywordsMarkov chain jump diffusion hybrid model Poisson process asymptotic expansion
2000 MR Subject Classification60J35 35C20 35K45
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