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Extremes of regularly varying Lévy-driven mixed moving average processes

  • Vicky Fasen (a1)

Abstract

In this paper, we study the extremal behavior of stationary mixed moving average processes of the form Y(t)=∫+×ℝ f(r,t-s) dΛ(r,s), t∈ℝ, where f is a deterministic function and Λ is an infinitely divisible, independently scattered random measure whose underlying driving Lévy process is regularly varying. We give sufficient conditions for the stationarity of Y and compute the tail behavior of certain functionals of Y. The extremal behavior is modeled by marked point processes on a discrete-time skeleton chosen properly by the jump times of the underlying driving Lévy process and the extremes of the kernel function. The sequences of marked point processes converge weakly to a cluster Poisson random measure and reflect extremes of Y at a high level. We also show convergence of the partial maxima to the Fréchet distribution. Our models and results cover short- and long-range dependence regimes.

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Copyright

Corresponding author

Postal address: Graduate Program in Applied Algorithmic Mathematics, Centre for Mathematical Sciences, Munich University of Technology, D-85747 Garching, Germany. Email address: fasen@ma.tum.de

References

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Extremes of regularly varying Lévy-driven mixed moving average processes

  • Vicky Fasen (a1)

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