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In this paper we consider multivariate Hawkes processes with baseline hazard and kernel functions that depend on time. This defines a class of locally stationary processes. We discuss estimation of the time-dependent baseline hazard and kernel functions based on a localized criterion. Theory on stationary Hawkes processes is extended to develop asymptotic theory for the estimator in the locally stationary model.
Locally stationary Hawkes processes have been introduced in order to generalise classical Hawkes processes away from stationarity by allowing for a time-varying second-order structure. This class of self-exciting point processes has recently attracte
This paper studies nonparametric estimation of parameters of multivariate Hawkes processes. We consider the Bayesian setting and derive posterior concentration rates. First rates are derived for L1-metrics for stochastic intensities of the Hawkes pro
This paper aims at providing statistical guarantees for a kernel based estimation of time varying parameters driving the dynamic of local stationary processes. We extend the results of Dahlhaus et al. (2018) considering the local stationary version o
We consider a stochastic individual-based model in continuous time to describe a size-structured population for cell divisions. This model is motivated by the detection of cellular aging in biology. We address here the problem of nonparametric estima
In this contribution we introduce weakly locally stationary time series through the local approximation of the non-stationary covariance structure by a stationary one. This allows us to define autoregression coefficients in a non-stationary context,