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July 1996 Stability of nonlinear Hawkes processes
Pierre Brémaud, Laurent Massoulié
Ann. Probab. 24(3): 1563-1588 (July 1996). DOI: 10.1214/aop/1065725193


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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Pierre Brémaud. Laurent Massoulié. "Stability of nonlinear Hawkes processes." Ann. Probab. 24 (3) 1563 - 1588, July 1996.


Published: July 1996
First available in Project Euclid: 9 October 2003

zbMATH: 0870.60043
MathSciNet: MR1411506
Digital Object Identifier: 10.1214/aop/1065725193

Primary: 60G55 , 60H20

Keywords: Hawkes processes , mutually exciting point processes , Point processes , stationary point processes , Stochastic intensity , Stochastic processes

Rights: Copyright © 1996 Institute of Mathematical Statistics


Vol.24 • No. 3 • July 1996
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