# Perfect Sampling of Hawkes Processes and Queues with Hawkes Arrivals

@article{Chen2021PerfectSO, title={Perfect Sampling of Hawkes Processes and Queues with Hawkes Arrivals}, author={Xinyun Chen}, journal={Stochastic Systems}, year={2021} }

In this paper we develop to our best knowledge the first perfect sampling algorithm for queues with Hawkes input (i.e., single-server queues with Hawkes arrivals and independent and identically distributed service times of general distribution). In addition to the stability condition, we also assume the excitation function of the Hawkes process has a light tail and the service time has finite moment-generating function in the neighborhood of the origin. In this procedure, we also propose a new…

## 7 Citations

Perfect Sampling of Multivariate Hawkes Processes

- Computer Science2020 Winter Simulation Conference (WSC)
- 2020

This paper presents a perfect sampling algorithm that can generate i.i.d. stationary sample paths of multivariate Hawkes process without any transient bias and provides an explicit expression of algorithm complexity in model and algorithm parameters and numerical schemes to find the optimal parameter set.

On the splitting and aggregating of Hawkes processes

- Computer Science, Mathematics
- 2021

A FCLT is proved for a multivariate Hawkes process under a random splitting and then aggregating scheme (under certain conditions, transforming into a Hawke process of a different dimension) and it is shown that random split Hawkes processes are again Hawkes.

Functional limit theorems for nonstationary marked Hawkes processes in the high intensity regime

- MathematicsStochastic Processes and their Applications
- 2021

Kalikow decomposition for counting processes with stochastic intensity and application to simulation algorithms

- Mathematics, Computer Science
- 2021

A new Kalikow decomposition is proposed for continuous time multivariate counting processes, on potentially inﬁnite networks and it is proved the existence of such a decomposition in various cases.

Conditional Uniformity and Hawkes Processes

- Mathematics
- 2022

Classic results show that the Hawkes self-exciting point process can be viewed as a collection of temporal clusters, where exogenously generated initial events give rise to endogenously driven…

The Co-Production of Service: Modeling Service Times in Contact Centers Using Hawkes Processes

- Computer ScienceSSRN Electronic Journal
- 2021

This paper proposes, develops, and compares new stochastic models for the co-production of service in a contact center, and finds that the bivariate Hawkes processes that incorporate the amount of information provided by each party or the sentiment expressed by the customer give the most accurate predictions.

Perfect Sampling of Multivariate Hawkes Process

- Computer Science
- 2020

This paper presents a perfect sampling algorithm that can generate i.i.d. stationary sample paths of multivariate Hawkes process without any transient bias and provides an explicit expression of algorithm complexity in model and algorithm parameters and numerical schemes to find the optimal parameter set.

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