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