Original Papers

Acta Mathematicae Applicatae Sinica

, Volume 20, Issue 1, pp 1-18

First online:

Asymptotic Expansions of Transition Densities for Hybrid Jump-diffusions

  • Yuan-jin LiuAffiliated withDepartment of Mathematics, Wayne State University Email author 
  • , G. YinAffiliated withDepartment of Mathematics, Wayne State University

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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.


Markov chain jump diffusion hybrid model Poisson process asymptotic expansion

2000 MR Subject Classification

60J35 35C20 35K45