Acta Mathematicae Applicatae Sinica

, Volume 20, Issue 1, pp 1–18

Asymptotic Expansions of Transition Densities for Hybrid Jump-diffusions

Original Papers

DOI: 10.1007/s10255-004-0143-5

Cite this article as:
Liu, Y. & Yin, G. Acta Mathematicae Applicatae Sinica, English Series (2004) 20: 1. doi:10.1007/s10255-004-0143-5

Abstract

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.

Keywords

Markov chain jump diffusion hybrid model Poisson process asymptotic expansion 

2000 MR Subject Classification

60J35 35C20 35K45 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of MathematicsWayne State UniversityDetroitUSA

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