A cluster process representation of a self-exciting process
- 1 September 1974
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 11 (03) , 493-503
- https://doi.org/10.1017/s0021900200096273
Abstract
It is shown that all stationary self-exciting point processes with finite intensity may be represented as Poisson cluster processes which are age-dependent immigration-birth processes, and their existence is established. This result is used to derive some counting and interval properties of these processes using the probability generating functional.Keywords
This publication has 3 references indexed in Scilit:
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- Asymptotic properties and equilibrium conditions for branching Poisson processesJournal of Applied Probability, 1969
- On the use of the characteristic functional in the analysis of some stochastic processes occurring in physics and biologyMathematical Proceedings of the Cambridge Philosophical Society, 1951