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Functional central limit theorems for stationary Hawkes processes and application to infinite-server queues
16 references·1 citing·44 second hop
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References

  • 1999Continuous Martingales and Brownian Motion6,200 cited
  • 2003Limit Theorems for Stochastic Processes2,529 cited
  • 1991Continuous Martingales and Brownian Motion1,957 cited
  • 2008Robust dynamic classes revealed by measuring the response function of a social system788 cited
  • 2002Stochastic-process limits : an introduction to stochastic-process limits and their application to queues468 cited
  • 2015Hawkes Processes in Finance459 cited
  • 2007Modelling security market events in continuous time: Intensity based, multivariate point process models397 cited
  • 2010Affine Point Processes and Portfolio Credit Risk373 cited
  • 2013Some limit theorems for Hawkes processes and application to financial statistics248 cited
  • 1993The Physics of the Mt/G/∞ Queue239 cited
  • 1965Limiting diffusion approximations for the many server queue and the repairman problem211 cited
  • 2007Martingale proofs of many-server heavy-traffic limits for Markovian queues183 cited
  • 2007Martingale proofs of many-server heavy-traffic limits for Markovian queues155 cited
  • 2016Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes136 cited
  • 2013Hawkes Process: Fast Calibration, Application to Trade Clustering, and Diffusive Limit

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129 cited
  • 2015Limit theorems for nearly unstable Hawkes processes127 cited
  • Cited by

    • 2018Infinite-server queues with Hawkes input45 cited