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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, 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.
    2. Spreij, Peter, 1998. "A representation result for finite Markov chains," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 183-186, June.

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