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Stability of Nonlinear Hawkes Processes

Pierre Bremaud and Laurent Massoulie
The Annals of Probability
Vol. 24, No. 3 (Jul., 1996), pp. 1563-1588
Stable URL: http://www.jstor.org/stable/2244985
Page Count: 26
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Stability of Nonlinear Hawkes Processes
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Abstract

We address the problem of the convergence to equilibrium of a general class of point processes, containing, in particular, the nonlinear mutually exciting point processes, an extension of the linear Hawkes processes, and give general conditions guaranteeing the existence of a stationary version and the convergence to equilibrium of a nonstationary version, both in distribution and in variation. We also give a new proof of a result of Kerstan concerning point processes with bounded intensity and general nonlinear dynamics satisfying a Lipschitz condition.

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