Asymptotic Expansions of Transition Densities for Hybrid Jump-diffusions

Authors: Liu, Yuan-jin¹; Yin, G.²

Source: Acta Mathematicae Applicatae Sinica, Volume 20, Number 1, March 2004 , pp. 1-18(18)

Publisher: Springer

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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; 60J35; 35C20; 35K45

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10255-004-0143-5

Affiliations: 1: Email: yuanjin@math.wayne.edu 2: Email: gyin@math.wayne.edu

Publication date: 2004-03-01