Summary
We prove an invariance principle in probability for planar point processes associated with extremal processes. The underlying sequence of random variables is absolutely regular, and satisfies a local asymptotic independence condition. A strong approximation for triangular arrays of such point processes is also stated. We apply these results to the weak convergence of intermediate quantile functions.
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Dabrowski, A.R. Extremal point processes and intermediate quantile functions. Probab. Th. Rel. Fields 85, 365–386 (1990). https://doi.org/10.1007/BF01193943
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DOI: https://doi.org/10.1007/BF01193943
Keywords
- Stochastic Process
- Probability Theory
- Extremal Point
- Mathematical Biology
- Point Process