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Self-exciting counting process systems with finite state space

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  • Spreij, Peter

Abstract

Stochastic systems with counting process output and a finite state space are considered. This leads to studying processes with finite state space that are Markovian with respect to the flow of [sigma]-algebras, that is generated by the counting process. It appears that there is a close relationship between the transition intensities of the Markov process and the intensity of the counting process. Some consequences for a stochastic realization problem are then studied.

Suggested Citation

  • Spreij, Peter, 1990. "Self-exciting counting process systems with finite state space," Stochastic Processes and their Applications, Elsevier, vol. 34(2), pages 275-295, April.
    • Handle: RePEc:eee:spapps:v:34:y:1990:i:2:p:275-295
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    Cited by:

    1. Spreij, Peter, 1998. "A representation result for finite Markov chains," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 183-186, June.
    2. Spreij, P., 1989. "Minimality and reducibility of conditionally poisson systems with finite state space," Serie Research Memoranda 0071, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.

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