Stability of nonlinear Hawkes processes
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.
Permanent link to this document: http://projecteuclid.org/euclid.aop/1065725193
Mathematical Reviews number (MathSciNet): MR1411506
Digital Object Identifier: doi:10.1214/aop/1065725193
Zentralblatt MATH identifier: 0870.60043