The Annals of Probability

Stability of nonlinear Hawkes processes

Pierre Brémaud and Laurent Massoulié

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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.

Article information

Ann. Probab., Volume 24, Number 3 (1996), 1563-1588.

First available in Project Euclid: 9 October 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G55: Point processes 60H20: Stochastic integral equations

Stochastic processes point processes stochastic intensity stationary point processes mutually exciting point processes Hawkes processes


Brémaud, Pierre; Massoulié, Laurent. Stability of nonlinear Hawkes processes. Ann. Probab. 24 (1996), no. 3, 1563--1588. doi:10.1214/aop/1065725193.

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