A Sufficient Condition for Continuous-Time Finite Skip-Free Markov Chains to Have Real Eigenvalues

Michael C. H. Choi () and Pierre Patie ()
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Michael C. H. Choi: Cornell University, School of Operations Research and Information Engineering
Pierre Patie: Cornell University, School of Operations Research and Information Engineering

A chapter in Mathematical and Computational Approaches in Advancing Modern Science and Engineering, 2016, pp 529-536 from Springer

Abstract: Abstract We provide a sufficient condition for the negative of the infinitesimal generator of a continuous-time finite skip-free Markov chain to have only real and non-negative eigenvalues. The condition includes stochastic monotonicity and certain requirements on the transition rates of the chain. We also give a sample path illustration of Markov chains that satisfy the conditions and its Siegmund dual. We illustrate our result by detailing an example which also reveals that our conditions are not necessary.

Keywords: Markov Chain; Sample Path; Infinitesimal Generator; Exponential Random Variable; Embed Markov Chain (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-30379-6_48

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DOI: 10.1007/978-3-319-30379-6_48

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