Displaying similar documents to “Point processes of minimal order statistics”

Central limit theorem for Gibbsian U-statistics of facet processes

Jakub Večeřa (2016)

Applications of Mathematics

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A special case of a Gibbsian facet process on a fixed window with a discrete orientation distribution and with increasing intensity of the underlying Poisson process is studied. All asymptotic joint moments for interaction U-statistics are calculated and the central limit theorem is derived using the method of moments.

Superposition of Diffusions with Linear Generator and its Multifractal Limit Process

Endre Iglói, György Terdik (2010)

ESAIM: Probability and Statistics

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In this paper a new multifractal stochastic process called Limit of the Integrated Superposition of Diffusion processes with Linear differencial Generator (LISDLG) is presented which realistically characterizes the network traffic multifractality. Several properties of the LISDLG model are presented including long range dependence, cumulants, logarithm of the characteristic function, dilative stability, spectrum and bispectrum. The model captures higher-order statistics by the cumulants....

Relationship between Extremal and Sum Processes Generated by the same Point Process

Pancheva, E., Mitov, I., Volkovich, Z. (2009)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: Primary 60G51, secondary 60G70, 60F17. We discuss weak limit theorems for a uniformly negligible triangular array (u.n.t.a.) in Z = [0, ∞) × [0, ∞)^d as well as for the associated with it sum and extremal processes on an open subset S . The complement of S turns out to be the explosion area of the limit Poisson point process. In order to prove our criterion for weak convergence of the sum processes we introduce and study sum processes...